ACT Preparation / Unit 14 ACT 1314 worked example, 60 to 90 seconds
Volume and Surface Area of a Solid
The idea
Solid-figure problems are solved in three steps. First, name the solid and decide whether the question asks for volume, what fills it, or surface area, what covers it. Second, read the dimensions, converting a diameter to a radius and making all units match. Third, apply the formula, and for a composite solid add or subtract the parts, counting only the surfaces that are exposed.
In practice
Worked example: a cylindrical tank has a diameter of 6 feet and a height of 8 feet, so its radius is 3. Volume: π × 9 × 8 = 72π, about 226 cubic feet. Painting the outside, top and bottom included: 2π × 9 + 2π × 3 × 8 = 18π + 48π = 66π, about 207 square feet.
Where people slip
Read what is painted or filled: a tank open at the top has one circle, not two, in its surface area, giving 57π instead of 66π.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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