Grade 10 · Geometry & measurement

Surface area and volume practice

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 15 surface area and volume problems our math games drill.

CCSS HSG.GMD.A.3CCSS 7.G.B.615 questions in the bank

Sample questions

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Question 1easy

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

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

Question 2easy

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

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

Question 3easy

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

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

Question 4easy

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

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

Question 5easy

Find the volume of a cylinder with radius $2$ and height $4$ . Use $\pi = 3$ .

$V = \pi r^2 h = 3 \times 4 \times 4 = 48$ .

Question 6easy

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

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

Question 7easy

Find the volume of a cylinder with radius $1$ and height $10$ . Use $\pi = 3$ .

$V = \pi r^2 h = 3 \times 1 \times 10 = 30$ .

Question 8easy

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

$V = \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \times 3 \times 27 = 108$ .

Tests that cover surface area and volume:

NAEP PSAT 8/9 SBAC LEAP 2025 NC EOG/EOC

More Grade 10 skills:

Surface area in context (SAT)Trig ratios and unit circle values Special right triangles Similar right triangle trigonometry Perimeter and arc length Midpoint formula Equation of a circle Circle theorems All Grade 10 practice →

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