Question

HELP PLS A circular hole has been drilled through a cylinder as shown. What is the approximate volume of the remaining solid? Use 3.14 for π

Answer 1

The question has some missing details such as ; Use cylindrical shells to find the volume of the remaining solid if the remaining solid is 8cm high. I have however solved it using the value of 8cm, you can use the same approach to solve for the volume irrespective of the value of the height you are given.

Explanation:

The detailed step by step analysis and appropriate Integration by susbtitution in order to get the volume of the remaining solid is as shown in the attached file.

Answer 2

126

Explanation:

`V = A * h = (1)/(4) * \pi * d^(2) * h = A * h = (1)/(4) * 3.14 * 36 * 5 = 141.3\\ \\V_(empty) = A * h = (1)/(4) * \pi * d^(2) * h = (1)/(4) * \pi * 4 * 5 = 15.7`

`V_(full) = V - V_(empty) = 141.3 - 15.7 = 125.6 \approx 126`