# MGSE8.G.9: Apply the Formulas for the Volume of Cylinders, Cones, and Spheres

**Math 8, Unit 3 Test** Name: **MGSE8.G.6 – G.8: Explain and apply the Pythagorean Theorem.**

**MGSE8.G.9: Apply the formulas for the volume of cylinders, cones, and spheres.**

- A glider flies 13 miles north from the airport and then 24 miles diagonally southeast. Approximately how far west does the glider have to fly to return to the airport?

- ≈10 milesB. ≈12 miles C. ≈20 miles D. ≈400 miles

- The screen on a computer monitorhas a length of 15 inches and a widthof 12 inches. What is the length of thediagonal to the nearest tenth of an inch?

- ≈9.0 inches B. ≈13.5 inches C. ≈21.7 inches D. ≈19.2 inches

- Given the lengths of the sides of a triangle, which of the following is not a right triangle?

A. / 5, 12, 13 / B. / 10, 12, 15 / C. / 6, 8, 10 / D. / 3, 4, 5

- The vertices of 3 squares are joined to form a right triangle. What is the area of the largest square?

- 41 cm2
- 10.5 cm2
- 56 cm2
- 46 cm2

- A leg of a right triangle is 30 meters long, and the hypotenuse is 35 meters long. What is the length of the other leg to the nearest tenth of a meter?

- ≈18.0 metersB. 30 meters C. ≈46.1 meters D. 325 meters

- How do you know which side of a right triangle is the hypotenuse?

- It is the shortest side.
- It is the side length between the shortest and longest side.
- It is either side that forms the right angle.
- It is the longest side and the side opposite the right angle.

- On a city map, a library is located at (6, 2) and a school is located at (0, 0). If each unit equals one mile, determine the distance (in a straight line) between the library and the school to the nearest tenth.

A. 40 mile

B. 2.8 miles

C. 6.2 miles

D. 5 miles

- Which of the following best represents the distance between a point located at (3, 5) and the origin?

A. 4 units

B. 8 units

C. units

D. units

- Determine the volume of the sphere.Use 3.14 for pi and round your answer to the nearest tenth.

- 3052.1 in.3

B. 338.1 in.3

C. 24416.64 in.3

D. 1356.5 in.3

- Determine the volume of the cone. Use 3.14 for pi and round your answer to the nearest tenth.

- 75.4 cm3

B. 1808.6 cm3

C. 452.2 cm3

D. 150.7 cm3

- Determine the volume of the cylinder. Use 3.14 for pi and round your answer to the nearest tenth.

A. 602.9 in.3

B. 150.8 in.3

C. 1,809.6 in.3

D. 201.1 in.3

- A can of juice is 6 inches high, and its base has a diameter of 4 inches. What is the volume of the can? Use 3.14 for pi and round your answer to the nearest tenth.

- 37.7 in.3B. 75.4 in.3C. 150.7 in.3D. 301.4 in.3

- Martina bought a paperweight in the shape of a cone. The radius was 12 cm and

the height was 9 cm. Find the volume. Use 3.14 for pi and round your answer

to the nearest tenth.

- 339.3 cm3B. 1,113.1 cm3C. 4,071.5 cm3D. 1,356.5 cm3

- A scoop of ice cream is in the shape of a sphere. The radius of the scoop of

ice cream is 2.5 inches. Find the volume of the ice cream. Use 3.14 for pi

and round your answer to the nearest tenth.

- 523.6 in.3B. 20.9 in.3C. 65.4 in.3D. 26.2 in.3

- A water trough for animals is shown to the right. What would have the greatest effect

on the volume of the water trough?

- Doubling pi.
- Doubling the radius.
- Doubling the hypotenuse.
- Doubling the height.

**Constructed Response**A support wire runs from the top of a tower to the ground. If the tower is 1200 feet tall and the wire is attached to the ground 500 feet from the base of the tower, how long is the support wire?**Justify your answer with supporting evidence**(e.g., a picture, work, and answer the question asked with your reasoning/explanation for your answer).

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