SAT question b0dc920d (Area and Volume)

Question

A manufacturer determined that right cylindrical containers with a height that is $4$ inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, $V$ , in cubic inches, of such containers, where $r$ is the radius, in inches?

69

Difficulty:Hard

A

$V = 4 π r^{3}$

B

$V = π (2 r)^{3}$

C

$V = π r^{2} + 4 π r$

D

$V = π r^{3} + 4 π r^{2}$

College Board · Accepted Answer

The correct answer is D. Choice D is correct. The volume, V , of a right cylinder is given by the formula V = π r^2 × h , where r represents the radius of the base of the cylinder and h represents the height. Since the height is 4 inches longer than the radius, the expression r + 4 represents the height of each cylindrical container. It follows that the volume of each container is represented by the equation V = π r^2 × (r + 4) . Distributing the expression π r^2 into each term in the parentheses yields V = π r^3 + 4 π r^2 .

CookSAT · Answer

Note: The calculator shows choice D expanded; the two expressions are identical for any r, confirming D is correct.

Explanation

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Why the other choices are wrong

SAT Question b0dc920d: Area and Volume answer and explanation with Desmos solution

Explanation

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Why the other choices are wrong