Question 46 Answer and Explanation _ACT April 2017 Form 74F Math Section

46. A box in the shape of a cube has an interior side length of 18 inches and is used to ship a right circular cylinder with a radius of 6 inches and a height of 12 inches. The interior of the box not occupied by the cylinder is filled with packing material. Which of the following numerical expressions gives the number of cubic inches of the box filled with packing material ？

F. $6{(18)}^{2}-2\pi(6)(12)-2\pi{(6)}^{2}$

G. $6{(18)}^{2}-2\pi(6)(12)$

H. ${18}^{3}-\pi(6){(12)}^{2}$

J. ${18}^{3}-\pi{(6)}^{2}(12)$

K. ${18}^{3}-\pi{(12)}^{3}$

Answer and Explanation

Your Answer is

Correct Answer is J

Explanation

First of all, the volume of the cube box is 18 cubes, so the volume occupied by the filling is 18³-12×π×6²