St J Surface area & Volume STUDY GUIDE Name _________________________________

Honors Geometry

SA = _________________ SA = _______________

V = __________________ V = _________________

2) Find the surface area and volume of a rectangular prism that is 3 cm by 4 cm by 5 cm.

3) Find the volume of a square pyramid that has base edges 6 inches long and a slant height of 5 inches.

4) A rectangular prism has a surface area of 448 cm2. Its length is 14 cm and its width is 6 cm. Find its height.

5) A cylinder has a diameter of 10 inches and a height of 5 inches. Find its surface area. Round your answer to

two decimal places.

6) Find the surface area of a cone that has a radius of 12 cm and a height of 20 cm. Round your answer to two

decimal places.

7) A cone has a volume of 112π cm3 and a height of 21 cm. Find its radius.

*Applications & Reasoning with SA and V

8)

9) A sphere with a diameter of 10 inches is placed in a cube. The sphere touches the lateral faces and bases

of the cube. How much larger is the volume of the cube than the volume of the sphere? Round your

answer to the nearest tenth.

4) Ms. Mathews’s dog, Digit, eats out of the automatic pet feeder shown below. If Digit eats 6% of the food in

the pet feeder each day, will the feeder hold enough food for 10 days? Explain your reasoning and show work to support your answer.

*Composite Figures Determine the indicated measurement of each composite figure. Round to the nearest 10th.

14) V= _______________ 15) SA = ____________ , V= _______________

***Oblique figures and solids of revolution

According to Cavalier’s principal, if a shape has identical crossections then the volumes are the same. The two oblique solids have

idential cross sections to the upright solid. Use the volume formulas to find the volume.

16) V = _______________________ 17) V = ___________________

19) a. If a rectangular prism is cut by the plane shown, what shape is

the cross section?

b. How would the plane need to slice the prism in order to create a

trapezoidal cross section?

20) a. The cylinder is cut by the plane that is perpendicular to the base of the cylinder. What is the shape of the

cross-section?

b. How would the plane need to slice the cylinder to create a circular cross section?

21) Use the picture to the right to answer the questions.

a. Describe the solid that is created when the figure above is rotated around the y-axis.

b. Find the volume of the solid.

c. Identify at least 3 two dimensional shapes created by cross sections of the solid.

***Density

22) A cylindrical candle with a radius of 3 centimeters and a height of 8 centimeters has a mass of 300

grams.

a) What is the density of the candle?

1.33 grams per cubic centimeter

b) Another candle made out of the same wax is formed into a cube. The mass of this candle is 475

grams. What are the dimensions of the cube?

7.1 cm.

c) Another candle made out of the same wax is formed into a cone. The diameter of the base of the

cone is 4 centimeters and the height of the cone is 12 centimeters. What is the mass of the cone

candle? 66.85 grams.