SURFACE AREA AND VOLUME

Instructions

1. Listen to teacher’s directions before continuing, raise your hand and ask questions every time you need.

2. Get your worksheet ready to record the information.

3. Go to the next page only if you have finished the one you are working on.

4. Do not rush, you have enough time to finish.

3-D Objects

PRISM

PYRAMID

CYLINDER

CONE

SPHERE

THREE-DIMENSIONAL OBJECTS

A three-dimensional object is a figure that has depth in addition to width and height.

The surface area of a 3-D object is the total area of all the faces of the figure.

SURFACE AREA

The volume is a measure of how much space a 3-D object takes up.

VOLUME

PRISM

A prism is a solid with two congruent parallel bases that are polygons.

PRISM

base

height

h

P = perimeter

B = area Surface Area SA = 2B + Ph

Volume V = B h

LATERAL AREA

PRISM

EXAMPLE

Find the surface area and volume of a slab of stone

measuring 3 m in length, 2 m in breadth and 25 cm in

thickness.

Solution:

l = 3 m

w = 2 m

h = 25 cm = 0.25 m

Surface area

SA= 2B + Ph = 2 (3 · 2) + (3+3+2+2)· 0.25 = 14.5 sq m.

Volume

V= l· w· h = 3· 2· 0.25 = 1.5 cu m.

PYRAMID

A pyramid is a solid having a polygonal base and triangle-shaped sides.

PYRAMID

lateral

height

l

base

P = perimeter

B = area

Surface Area SA = B + 1/2 Pl

Volume V = 1/3 B h

LATERAL AREA

PYRAMID

CYLINDER

A cylinder is a solid with two circular bases that are parallel.

CYLINDER

height

h

radius

r

Surface Area SA = 2πr2+2πrh

Volume V = π r2 h

LATERAL AREA

CYLINDER

CONE

A cone is solid having a circular base and a single vertex.

CONE

radius

r

lateral

height

lSurface Area SA = πr2 + πrl

Volume V = 1/3 πr2 h

LATERAL AREA

CONE

SPHERE

A sphere is a solid having all of its points the same distance from its center, this distance is called radius.

SPHERE

radius

r Surface Area SA = 4 π r2

Volume V = 4 /3 π r3

SPHERE

FORMULAS

Surface Area Volume

Prism 2B + Ph B h

Pyramid B + 1/2 Pl 1/3 B h

Cylinder 2πr2 + 2πr h π r2 h

Cone πr2 + πrl 1/3 πr2 h

Sphere 4 π r2 4 /3 π r3

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