Surface area and volume Practice Questions (Grade 10)

Surface area and volume. Game on.

Surface area and volume is a grade 10 math skill aligned to Common Core standard HSG.GMD.A.3 and 7.G.B.6: use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 30 surface area and volume problems our math games drill.

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Warm-upeasy

Find the volume of a cone with radius $2$ and height $6$ . Use $\pi = 3$ .

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 4 \times 6 = 24$ .

Mid-gameeasy

Find the volume of a cylinder with radius $2$ and height $5$ . Use $\pi = 3$ .

$V = \pi r^{2} h = 3 \times 4 \times 5 = 60$ .

Mid-gameeasy

A tent is a square pyramid with base side $6$ feet and height $4$ feet. Each camper needs $16$ cubic feet of air.

How many campers can the tent hold?

The tent holds $V = \dfrac{1}{3}Bh = \dfrac{1}{3}(6)^{2}(4) = 48$ cubic feet. Then $48 \div 16 = 3$ campers.

Mid-gameeasy

Find the volume of a sphere with radius $2$ . Use $\pi = 3$ .

$V = \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \times 3 \times 8 = 32$ .

Mid-gameeasy

Find the volume of a cone with radius $3$ and height $5$ . Use $\pi = 3$ .

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 9 \times 5 = 45$ .

Mid-gameeasy

Find the volume of a cylinder with radius $3$ and height $2$ . Use $\pi = 3$ .

$V = \pi r^{2} h = 3 \times 9 \times 2 = 54$ .

Mid-gameeasy

Find the surface area of a sphere with radius $1$ . Use $\pi = 3$ .

$SA = 4 \pi r^{2} = 4 \times 3 \times 1 = 12$ .

Buzzer beatereasy

Find the volume of a cone with radius $2$ and height $9$ . Use $\pi = 3$ .

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 4 \times 9 = 36$ .

Surface area and volume. Game on.

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