Solid Geometry.docx

7/22/2019 Solid Geometry.docx

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SolidGeom

QuestText Choice1 Choice2 Choice3 Choice4 SubjA _______ section of a surface of revolution is the section containing the

axis of revolution. Meridian Central Median Right SolidGeometry

A certain Chinese coin, 1/2 in. in diameter and 1/19 in. thick is pierced by

a square hole which is 1/3 in. on a side. Find the AMount of metal in the

coin.0.011295 cu. in. 1.025484 cu. in. 2.158051 cu. in. 0.598471 cu. in. Solid

Geometry

A circle with radius 6 cm has half its area removed by cutting off a border

of uniform width. Find the width of the border. 1.76 cm 1.35 cm 1.98 cm 2.03 cm SolidGeometry

A closed cylindrical tank has a capacity of 16 cu.m. Determine the radius

and height of the tank that requires minimum amount of materials used. 2 m., 4 m 2 m., 6 m 2 m., 3 m 3 m., 4.5 m SolidGeometry

A closed cylindrical tank has a capacity of 576.56 m^3. Find the minimum

surface area of the tank. 383.40 m3 516.32 m3 412.60 m3 218.60 m3 SolidGeometry

A coffee pot is 5 in. deep, 4 in. in diameter at the top and 5 in. in

diameter at the bottom. How many cup of coffee will it hold if 6 cups

equal a quart?11 cups 10 cups 12 cups 13 cups Solid

Geometry

A cone and a cylinder have the same height and the same volume. Find

the ratio of the radius of the cone to the radius of the sylinder.1.732 0.577 0.866 1.414 Solid

Geometry

A cylindrical boiler is to have a volume of 1,340 cu. ft. The cost of the

metal sheets to make the boiler should be minimum. What should be its

base diameter in feet?11.95 7.08 8.08 10.95 Solid

Geometry

A drop hammer weighing 40 KN is dropped freely and drives a concrete

pile 150 mm into the ground. The velocity of the drop hammer at impact

is 6 m/sec. What is the average resistance of the soil in KN?489.3 542.4 384.6 248.7 Solid

Geometry

A grain elevator in the form of a frustum of a right circular cone is 24 ft.

high, and the radii of its bases are 10 ft. and 5 ft., respectively. How many

bushels of wheat will it hold if 1 cu. ft. equals 1 bu.?3518.6 bu. 3347.5 bu. 2948.9 bu. 3625.1 bu. Solid

Geometry

A hole 6 in. in diameter was bored through a sphere 10 in. in diameter.

Find the volume of the part cut out.255.52 cu. in 210.48 cu. in 224.96 cu. in 230.25 cu. in Solid

Geometry

A normal window is in the shape of a rectangle surrounded by a semi-

circle. If the perimeter of the window is 71.416, what is the radius and

10 22 13 27 SolidGeometry


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SolidGeom

QuestText Choice1 Choice2 Choice3 Choice4 Subjthe height of the rectangular portion so that it will yield a window

admitting the most light?

A piece of plywood for a billboard has an area of 24 sq. ft. The margins at

the top and bottom are 9 in. and at the sides are 6 in. Determine the size

of the plywood for maximum dimensions of the painted area.4 x 6 4 x 8 3 x 8 3 x 4 Solid

Geometry

A rectangular box is to have a square base and an open top, and is to be

constructed from 75 sq. m. of material. If the volume is to be as large as

possible, what should be the height of the box?2.5 1.2 3.2 4.4 Solid

Geometry

A rectangular box with a square base and open top is to be made. Find

the volume of the largest box that can be made from 432 sq. m. of

material.4 m^3 8 m^3 6 m

12m^3 6 m^3 SolidGeometry

A rectangular box with square base and open at the top is to have a

capacity of 16,823 cu.cm. Find the the height of the box that requires

minimum amount of material required.16.14 12.14 14.16 15.16 Solid

Geometry

A regular hexagonal pyramid has a slant height of 4 cm and the length of

each side of the base is 6 cm. Find the lateral area.72 cm^2 82 cm^2 62 cm^2 92 cm^2 Solid

Geometry

A reservoir 10 ft. deep is in the form of the frustum of an inverted square

pyramid with bases 100 and 90 ft. on a side, respectively. How long will it

require an inlet pipe to fill this reservoir if the water poured in at the rate

of 200 gal. per minute?56.312 hr. 60.254 hr 52.016 hr 53.165 hr Solid

Geometry

A reservoir is in the form of a frustum of a cone, 68 ft. across the top, 35

ft. across the bottom, and 18 ft. deep. Find the cost of lining it with tile at

$1 per square foot.$ 4,912.90 $ 5,486.15 $ 4,201.58 $ 6,015.26 Solid

Geometry

A sector is cut of a circular disk of radius and the remaining part of the

disk is bent up so that the two edges join and a cone is formed. What is

the largest volume for the cone?2/3 pi pi pi pi Solid

Geometry

A solid has a circular base of radius r. Find the volume of the solid ifevery plane is perpendicular to a fixed diameter is a square 16r3 / 3 17r3 / 3 22r3 / 3 13r3 / 3 SolidGeometry

A solid has a circular base of radius 4 units. Find the volume of the solid if 147.80 136.40 125.36 156.40 Solid


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SolidGeom

QuestText Choice1 Choice2 Choice3 Choice4 Subjevery plane section perpendicular to a particular fixed diameter is an

equilateral triangle. GeometryA solid of revolution of a parabola is known as Paraboloid Hyperboloid Catenoid Conoid Solid

Geometry

A spherical shell 2 in. thick has an outer diameter of 12 in. Find the

volume of the material of which it is made. 636.70 cu. in. 548.25 cu. in. 154.25 cu. in. 758.21 cu. in. SolidGeometry

A stone is dropped into a circular tub 40 in. in diameter, causing the

water therein to rise 20 in. What is the volume of the stone? 14.545 cu. ft. 15.246 cu. ft. 13.254 cu. ft. 12.248 cu. ft. SolidGeometry

A trapezoid has an area of 36 sq. m. and altitude of 2 m. Its two bases

have ratio of 4:5. What are the lengths of the bases. 16 and 20 12 and 15 8 and 10 20 and 25 SolidGeometry

A wooden ball 2 ft. in diameter weighs 200 lb. Find the diameter of ball

of the same material which weighs 50 lb. 1.2599 ft. 2.0015 ft. 0.3458 ft. 3.0158 ft. SolidGeometry

A woodman chops halfway through a tree having a diameter of 2m. One

face of the cut being horizontal and the other inclined at 60. Find the

volume of wood cut out1.155 cu. m 4.532 cu. m 3.823 cu. m 2.453 cu. m Solid

Geometry

An anchor ring is formed by revolving a circle 2 in. in diameter about a

line lying in the plane of the circle and at a distance of 7 in. from its

center. Find the volume of the solid formed.138.18 cu. in. 124.02 cu. in. 105.12 cu. in. 140.25 cu. in. Solid

Geometry

An open top rectangular tank with square bases is to have a volume of 10

cu. m. The material for its bottom is to cost 15 cents per square meter

and that for the sides 6 cents per square meter. Find the most

economical dimensions for the tank.

2 x 2 x 2.5 2 x 3 x 2.5 2 x 5 x 2.5 2 x 4 x 2.5 SolidGeometry

Assuming that a city has 400 miles of water pipes and that the average

diameter of the pipes is 1 ft., how much water is required fill this entire

system?12,408,000 gal. 10,254,032 gal. 9,254,015 gal. 13,254,160 gal. Solid

Geometry

Each of the faces of a regular hexahedron is a _________. Square Triangle Rectangle Hexagon SolidGeometry

Each side of a cube is increased by 1%. By what percent is the volume of

the cube increased? 3.03% 2.8% 1.21% 3.5% SolidGeometry


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SolidGeom

QuestText Choice1 Choice2 Choice3 Choice4 SubjEqual volumes of the two different liquids evaporated at different but

constant rates. If the first is totally evaporated in 6 weeks and the second

in 5 weeks, when will the second be one-half the volume of the first?30/7 weeks 3.5 weeks 4 weeks 3 weeks Solid

Geometry

Find the approximate increase by the use of differentials, in the volume

of the sphere if the radius increases from 2 to 2.05 in one second.2.51 2.12 2.86 2.25 Solid

GeometryFind the diameter of the base of a pint tin can whose height is 4 in. (231

cu. in. 1 gal.)? 3.086 in 5.254 in 1.569 in 4.025 in SolidGeometryFind the largest area of a rectangle that can be inscribed in the ellipse

4x^2 + 9y^2 = 36. 12 16 20 25 SolidGeometry

Find the minimum amount of thin sheet that can be made into a closed

cylinder having a volume of 108 cu. in. in square inches. 5.5 7.5 3.5 9.5 SolidGeometryFind the volume of a sphere circumscribed about a cylinder of revolution,

the radius of whose base is 3 in. and whose altitude in 8 in. 523.95 cu. in. 552.25 cu. in. 586.15 cu. in. 500.15 cu. in. SolidGeometry

Find the volume of the parallelepiped whose edges are represented by A

= 2i- 3j + 4k, B = i + 2j - k and C = 3i-j + 2k. 7 6 8 5 SolidGeometryFormerly, for a package to go by parcel post, the sum of its length and

girth could not exceed 120 cm. Find the dimensions of the rectangular

package of greatest volume that could be sent.20 x 20 x 40 20 x 20 x 20 20 x 40 x 10 40 x 20 x 30 Solid

GeometryFour squares are cut out of rectangular cardboard 50 cm. by 80 cm. in

dimension and the remaining piece is folded into a closed rectangular

box with two extra flaps tucked in. What is the largest possible volume

for such a box?

9000 6000 7000 8000 SolidGeometry

From a cylindrical glass 6 in. high and 3 in. in diameter, water is poured

by tilting the glass until the highest point of the bottom of the glass lies

in the plane of the water surface. How much water remains?21.206 cu. in. 22.987 cu. in. 15.169 cu. in. 18.214 cu. in. Solid

GeometryGiven a sphere of diameter, d. What is the percentage increase in its

volume when the surface area increases by 21%?33% 10% 21% 5% Solid

Geometry

Given a sphere of the diameter, d. What is the percentage increase in its

diameter when the surface area increase by 21%? 10% 5% 21% 33% SolidGeometry


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SolidGeom

QuestText Choice1 Choice2 Choice3 Choice4 SubjHow many cubic feet of water are in a pond covering 200 acres if its

average depth is 20 ft.? 174,240,000 cu. ft. 173,240,000 cu. ft. 175,240,000 cu. ft. 176,240,000 cu. ft. SolidGeometryHow many cubic inches of lumber does a stick contain if it is 4 in. by 4 in.

at one end, 2 in. by 2 in. at the other end, and 16 ft. long? 1792 cu. in 1824 cu. in 1722 cu. in 1524 cu. in SolidGeometryHow many square feet of tin are required to make a funnel, if the of the

top and bottom are 28 in. and 14 in. respectively, and the height 24 in.? 11.454 sq. ft. 12.025 sq. ft. 13.254 sq. ft. 14.205 sq. ft. SolidGeometryIf a bell 4 in. in height, 3 in. in external diameter, and in. thick weighs 2

lb., what should be the dimension of a bell of the same proportions that

would weigh 2000 lb.?Height = 40 in.

diameter = 30 in.

thickness = 2.5 in.Height = 50 in.

diameter = 30 in.


diameter = 34 in.


diameter = 39 in.

thickness = 3.5 in.Solid

GeometryIf a piece of brass 8 by 6 by 12 in. is drawn out into a wire us in. in

diameter, what will be the length of the wire? 55,004 ft. 49,215 ft. 50,000 ft. 56,548 ft. SolidGeometryIt is a polyhedron that has a polygon as its base and sides that consist of

triangles having a common vertex, called the apex. Pyramids Prism Sphere Hexagon SolidGeometryIt is a polyhedron that has parallel and congruent polygons, called bases,

for two faces and parallelograms for all other faces. Prism Hexagon Sphere Rhombus SolidGeometryIt is a prism with circular bases. Cylinder Prism Sphere Pyramids Solid

GeometryIt is a two-dimensional curves created by slicing a plane through a three-

dimensional hollow cone. Conic sections Parabola Circle Hyperbola SolidGeometryIt is desired to cut off a piece of lead pipe 2 in. in outside diameter and

in. thick, so that it will melt into a cube of edge 4 in. How long a piece will

be required?46.564 in 43.254 in 35.125 in 50.251 in Solid

GeometryOne of the diagonals of a rhombus is 25 units and its area is 75 square

units. Determine the length of the sides. 12.86 units 15.47 units 12.58 units 18.25 units SolidGeometryOne side of a regular octagon is 2. Find the area of the region inside the

octagon. 19.3 13.9 31.9 91.3 SolidGeometrySoap kettles used in the commercial manufacture of soap are as a rule

large cylindrical vat, 500,000 lb. or more of soap being made in a single

heating. Find the capacity of such a kettle having an inside diameter of

534,380 lb 544,587 lb 509,547 lb 558,461 lb SolidGeometry


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SolidGeom

QuestText Choice1 Choice2 Choice3 Choice4 Subj18 ft. and an altitude of 30 ft.The altitude of a right circular cylinder is twice the radius of the base. The

altitude is measured as 12 cm. With a possible error of 0.005 cm. Find

the approximate error in the calculated volume of the cylinder.0.188 cm^3 0.144 cm^3 0.104 cm^3 0.126 cm^3 Solid

GeometryThe arch of an underpass is a semi ellipse 60 ft wide and 20 ft high. Find

the clearance at the edge of a lane if the edge is 20 ft from the middle. 14.9 ft 12 ft 15.2ft 20 ft SolidGeometryThe edges of a rectangular box are to be reinforced with narrow metal

strips. If the box will have a volume of 8 m3, what would its dimensions

be to require the least total length of strips?4 x 4 x 4 3 x 3 x 3 2 x 2 x 2 2 x 2 x 4 Solid

GeometryThe inside of a vase is an inverted cone 2.983 in. across the top and 5.016

in. deep. If a heavy sphere 2.428 in. in diameter is dropped into it when

the vase is full of how much water will overflow?6.9208 cu. in. 5.0489 cu. in. 10.254 cu. in. 8.0548 cu. in. Solid

GeometryThe lateral area of the right circular water tank is 92 sq. cm. And its

volume is 342 cu.m., determine its radius. 7.43 cm 5.56 cm 6.05 cm 7.28 cm SolidGeometryThe parabolic reflector of an automobile headlight is 12 cm. in diameter

and 4 cm. in depth. What is the surface area in sq. cm?153.94 146.84 142.64 152.64 Solid

GeometryThe volume of a sphere 88.5cu in, find the volume of a cube inscribed in

it. 31.784 cu. in. 40.589 cu. in. 52.015 cu. in. 48.158 cu. in. SolidGeometryThe volume of any solid of revolution is equal to the generating area

times the circumference of the circle described by the centroid of the

area. This is known asSecond proposition of

Pappus First proposition ofPappus Cavalieris theorem Simpsons rule SolidGeometryTwo spheres of lead, of radii 2 and 3 in., respectively, are melted into a

cylinder of revolution of radius 1 in. Find the altitude of the cylinder. 46.67 in. 64.02 in. 44.13 in. 50.12 in. SolidGeometryWhat is the area of the largest rectangle that can be inscribed in a semi-

circle of radius 10? 100 sq. units 50 sq. units 1,000 sq. units 500 sq. units SolidGeometryWhen a catenary (y = cosh x) is rotated about its axis of symmetry, it

generates a solid calledCatenoid Conoid Paraboloid Hyperboloid Solid

GeometryWhen the ellipse is rotated about its shorter axis, the ellipsoid is Prolate Paraboloid Spheroid Oblate Solid

Geometry


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Solid Geometry.docx