Question

a solid wooden post in the shape of a right rectangular prism measuring 9 cm by 10 cm by 28 cm is drilled with a cylindrical hole of diameter 8 cm. find the volume of the post after the hole has been drilled. round your answer to the nearest tenth if necessary. (note: diagram is not drawn to scale.)

Explanation:

Step1: Calculate prism volume

$V_{\text{prism}} = 9 \times 10 \times 28 = 2520$ $\text{cm}^3$

Step2: Find cylinder radius

$r = \frac{8}{2} = 4$ $\text{cm}$

Step3: Calculate cylinder volume

$V_{\text{cylinder}} = \pi r^2 h = \pi \times 4^2 \times 28 = 448\pi \approx 1407.43$ $\text{cm}^3$

Step4: Subtract volumes for final value

$V_{\text{final}} = V_{\text{prism}} - V_{\text{cylinder}} = 2520 - 1407.43$

Answer:

$1112.6$ $\text{cm}^3$