Volume word problems (ACT). Game on.

Volume word problems (ACT) is a grade 9 math skill aligned to Common Core standard HSG.GMD.A.3: 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 10 volume word problems (act) problems our math games drill.

CCSS HSG.GMD.A.310 questions in the bank
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Warm-upeasy

A storage shed is shaped like a rectangular prism that is 1212 feet long, 88 feet wide, and 55 feet tall. What is the volume of the shed's interior, in cubic feet?

For a rectangular prism, V=ℓwh=12×8×5=480V = \ell w h = 12 \times 8 \times 5 = 480 cubic feet.

Mid-gameeasy

A grain silo is shaped like a right circular cylinder with a radius of 44 feet and a height of 1010 feet. What is the volume of the silo, in cubic feet?

V=πr2h=π(4)2(10)=160πV = \pi r^{2} h = \pi (4)^{2}(10) = 160\pi cubic feet.

Mid-gameeasy

A culvert pipe is a right circular cylinder with an inside diameter of 1212 inches and a length of 2020 inches. What is the volume of the pipe's interior, in cubic inches?

The radius is 66 inches. V=πr2h=π(6)2(20)=720πV = \pi r^{2} h = \pi (6)^{2}(20) = 720\pi cubic inches.

Mid-gameeasy

A community pool is a rectangular prism 2424 feet long, 1818 feet wide, and 66 feet deep when filled to the planned level. How many cubic feet of water does the pool hold at that level?

V=ℓwh=24×18×6=2,592V = \ell w h = 24 \times 18 \times 6 = 2{,}592 cubic feet.

Mid-gamemedium

An ice machine makes spherical ice balls with a diameter of 66 centimeters. What is the volume of one ice ball, in cubic centimeters?

The radius is half the diameter: r=3r = 3 cm. Then V=43πr3=43π(3)3=36πV = \dfrac{4}{3}\pi r^{3} = \dfrac{4}{3}\pi (3)^{3} = 36\pi cubic centimeters.

Mid-gamemedium

A traffic cone is shaped like a right circular cone with a base diameter of 1010 inches and a height of 1212 inches. What is the volume of the cone, in cubic inches?

The radius is 55 inches. V=13πr2h=13π(5)2(12)=100πV = \dfrac{1}{3}\pi r^{2} h = \dfrac{1}{3}\pi (5)^{2}(12) = 100\pi cubic inches.

Mid-gamemedium

A cylindrical rain barrel has an inside radius of 33 feet. After a storm, the water level rises 44 inches. What is the volume of the added water, in cubic feet?

Convert 44 inches to 13\dfrac{1}{3} foot. V=πr2h=π(3)2(13)=3πV = \pi r^{2} h = \pi (3)^{2}\left(\dfrac{1}{3}\right) = 3\pi cubic feet.

Buzzer beaterhard

A concrete drainage pipe is a hollow right circular cylinder. The outer radius is r1=6r_1 = 6 meters, the inner radius is r2=4r_2 = 4 meters, and the pipe is 55 meters long. What is the volume of concrete in the pipe wall, in cubic meters?

Wall volume is outer minus inner: V=πh(r12−r22)=π(5)(62−42)=π(5)(20)=100πV = \pi h(r_1^{2} - r_2^{2}) = \pi (5)(6^{2} - 4^{2}) = \pi (5)(20) = 100\pi cubic meters.

Tests that cover volume word problems (act):
NAEPSATACTLEAP 2025NC EOG/EOC
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