Study on the flyACTMathematicsSurface area and volume of solids
Mathematics
Volume measures the space inside a solid, while surface area adds up the areas of every face, and Surface area and volume of solids tests both.
Expect rectangular boxes, cylinders, cones and spheres; the ACT usually supplies the less familiar formulas, such as the volume of a sphere, four-thirds pi r cubed. Some questions run a formula backward, giving the volume and asking for the radius or diameter.
Scaling is a favorite twist: multiplying every length by k multiplies area by k squared and volume by k cubed, not by k. Painting or wrapping problems may leave out a hidden face, so read which surfaces count.
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 38 Surface area and volume of solids questions in the app
Harder than the exam: ACT Challenge · Competition-style problems
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