SAT Math Tutorial
Geometry| Solid Geometry| Level 4
Intro
This is question 8 from Lesson 20 of my book The Scholarly Unicorn’s SAT Math Advanced Guide.
Topic: Geometry
Subtopic: Solid Geometry
Level: 4
Sample Problem
The volume of right circular cylinder C is V cubic inches. Right circular cylinder D has twice the height and half the radius of right circular cylinder C. Which of the following expresses the volume of right circular cylinder D in terms of V ?
Solution
Algebraic solution: The volume of cylinder C is V = πr^2 h, where r is the radius of C and h is the height of C. It follows that the radius of cylinder D is r/2 and the height of cylinder D is 2h. So, the volume of cylinder D is W = π(r/2)^2 (2h) = π r^2/4 ⋅ 2h = (πr^2 h)/2 = V/2, choice D.
* Quick solution: In the formula for the volume of a cylinder, r is squared. It follows that multiplying the radius by 1/2 multiplies the volume by (1/2)^2 = 1/4. Since h does not have any power, multiplying the height by 2, multiplies the volume by 2. So, when we take half of the radius and double the height, the volume is multiplied by 1/4 ⋅ 2 = 1/2. Therefore, the answer is choice D.
Note: This problem can also be solved by picking numbers. I leave the details of this solution to the reader.
Here is a video solution for this problem:
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