Study on the flyACTMathematicsSurface area and volume of solids
Practice 37 Surface area and volume of solids questions in the app
Surface area and volume of solids on the ACT Mathematics test covers rectangular boxes, spheres, and similar solids.
Students must find volume after a linear scale factor is applied, recover a sphere's diameter from its volume, and compute the painted surface of a block when a face is left unpainted. Questions typically give dimensions in feet or inches, ask for a nearest-cubic-unit volume, or keep π in the given volume.
Traps include applying the scale factor only once rather than cubing it, mixing radius with diameter, and counting an unpainted face. Answer choices are numbers of square or cubic units, sometimes still involving π.
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 1Easier
A rectangular wooden block measures 12 inches by 7 inches by 5 inches. Every face except the 12-inch-by-7-inch bottom is painted. What is the area, in square inches, of the painted surface?
Answer: C — 274
All 6 faces have area square inches. The unpainted bottom has area , so the painted area is square inches.
Question 2Mid
A rectangular container measures 5 by 3 by 2 feet. A similar container has every linear dimension multiplied by 1.6. To the nearest cubic foot, what is the larger container’s volume?
Answer: C — 123
Volumes of similar solids scale by the cube of the linear scale factor. The new volume is , which is approximately 123 cubic units.
Question 3Mid
A sphere has a volume of cubic centimeters. What is the diameter of the sphere, in centimeters?
Answer: C — 12
Solving gives , so centimeters. The diameter is centimeters.
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
Practice 37 Surface area and volume of solids questions in the app
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