Volume of Spheres

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Show your work for each problem.

1.
Which formula gives the volume of a sphere with radius $r$ ?
1. a) $V = \frac{4}{3}\pi r^3$
2. b) $V = \frac{1}{3}\pi r^2 h$
3. c) $V = \pi r^2 h$
4. d) $V = 4\pi r^2$
2.
A sphere has a radius of $3$ cm. Its volume is $V = \square\,\pi$ cm³. What number goes in the box?
3.
A ball has a diameter of $10$ cm. Which value of $r$ do you put into $V = \frac{4}{3}\pi r^3$ ?
1. a) $2.5$ cm
2. b) $5$ cm
3. c) $20$ cm
4. d) $10$ cm
4.
Find the volume of a sphere with radius $6$ m. Leave the answer in terms of $\pi$ .
5.
A sphere has a volume of $500$ cm³. It is cut exactly in half through its center. What is the volume of one hemisphere, in cm³?
6.
A ball has a diameter of $6$ cm. Find its volume using $\pi \approx 3.14$ . Round to the nearest hundredth.
7.
The radius of a sphere is doubled. What happens to its volume?
1. a)It doubles
2. b)It becomes 8 times as big
3. c)It becomes 4 times as big
4. d)It becomes 6 times as big
8.
A marble has a radius of $1.5$ cm. Its volume is $V = \square\,\pi$ cm³. What number goes in the box? (Write it as a decimal.)
9.
A salad bowl is a hemisphere with an inside radius of $9$ cm. How much can it hold? Use $\pi \approx 3.14$ and round to the nearest hundredth.
10.
A sphere has a volume of $288\pi$ cm³. What is its radius in cm?
11.
A sphere fits exactly inside a cylinder (same radius, and the cylinder's height equals the sphere's diameter). What fraction of the cylinder's volume does the sphere fill?
1. a) $\frac{1}{3}$
2. b) $\frac{2}{3}$
3. c) $\frac{3}{4}$
4. d) $\frac{1}{2}$
12.
A basketball has a diameter of $24$ cm. Find its volume using $\pi \approx 3.14$ . Round to the nearest whole cm³.
13.
A round water tank is a sphere with a diameter of $2$ m. Find its volume using $\pi \approx 3.14$ . Round to the nearest hundredth of a m³.
14.
A sphere has a volume of $972\pi$ cm³. Find its radius.
15.
A ball with radius $6$ cm is packed in a cylindrical box with radius $6$ cm and height $12$ cm. How much empty space is left in the box? Leave the answer in terms of $\pi$ .
16.
Which holds more: a sphere with radius $3$ cm or a cube with edges of $5$ cm? (Use $\pi \approx 3.14$ .)
1. a)The sphere
2. b)It cannot be decided
3. c)They hold the same amount
4. d)The cube
17.
Eight small chocolate balls, each with radius $1$ cm, are melted and made into one big ball. What is the radius of the big ball?
18.
A dome shaped like a hemisphere has a volume of $144\pi$ m³. What is its radius in m?