Spheres and Hemispheres: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

A ball has volume $288\pi\text{ cm}^3$ . What is its radius?

Answer choices for question 1 A 3 cm B 6 cm C 8 cm D 9 cm
2

A sphere has area $324\pi\text{ cm}^2$ . What is its diameter?

Answer choices for question 2 A 9 cm B 27 cm C 81 cm D 18 cm
3

A hemisphere has radius 2.5 cm. What is its exact volume?

Answer choices for question 3 A $\frac{125\pi}{12}\text{ cm}^3$ B $\frac{125\pi}{6}\text{ cm}^3$ C $\frac{25\pi}{2}\text{ cm}^3$ D $\frac{125\pi}{8}\text{ cm}^3$
4

A solid hemisphere has total boundary area $243\pi\text{ cm}^2$ , including its flat base. What is its radius?

Answer choices for question 4 A 3 cm B $9\sqrt{\frac32}\text{ cm}$ C 9 cm D 81 cm
5

The disk bounded by a sphere's great circle has area $36\pi\text{ cm}^2$ . What is the sphere's area?

Answer choices for question 5 A $144\pi\text{ cm}^2$ B $36\pi\text{ cm}^2$ C $72\pi\text{ cm}^2$ D $108\pi\text{ cm}^2$
6

A ball has radius 10 cm. A plane lies 8 cm from its center, measured perpendicularly. What is the area of the filled section?

Answer choices for question 6 A $6\pi\text{ cm}^2$ B $36\pi\text{ cm}^2$ C $64\pi\text{ cm}^2$ D $164\pi\text{ cm}^2$
7

In the hemisphere comparison, the cylinder radius and height are 6 cm. The removed cone apex is at the bottom center and its top radius is 6 cm. What section area remains at height 2 cm above the bottom?

Answer choices for question 7 A $4\pi\text{ cm}^2$ B $20\pi\text{ cm}^2$ C $36\pi\text{ cm}^2$ D $32\pi\text{ cm}^2$
8

A comparison cylinder and removed cone each have positive radius R and height R. The cone apex is at the bottom, where height z is zero. Which formula gives the cone section radius for every height z from zero to R?

Answer choices for question 8 A $R-z$ B $R$ C $z$ D $\sqrt{R^2-z^2}$
9

A ball is cut through its center into two solid hemispheres. How does the volume of either piece compare with the original volume?

Answer choices for question 9 A It is one-third the original volume B It is one-half the original volume C It is two-thirds the original volume D It equals the original volume
10

The largest plane section of a ball has disk area $49\pi\text{ cm}^2$ . What is the ball volume?

Answer choices for question 10 A $\frac{1372\pi}{3}\text{ cm}^3$ B $\frac{686\pi}{3}\text{ cm}^3$ C $196\pi\text{ cm}^3$ D $343\pi\text{ cm}^3$
11

A ball has volume $36\pi\text{ cm}^3$ . What is the circumference of a great circle?

Answer choices for question 11 A $3\pi\text{ cm}$ B $9\pi\text{ cm}$ C $6\pi\text{ cm}$ D $12\pi\text{ cm}$
12

An ideal spherical surface has radius 0.8 m. What is its exact area?

Answer choices for question 12 A $0.64\pi\text{ m}^2$ B $1.28\pi\text{ m}^2$ C $3.2\pi\text{ m}^2$ D $2.56\pi\text{ m}^2$