Find the volume of the figure
Attached Figure / Diagram
A
\(\frac{a \pi^2}{3} (x + 3y) \)
B
a\(\pi ^2\)y
C
\(\frac{a \pi ^2}{3}\)(y + x)
D
(\(\frac{1}{3} a \pi ^2 x + y\))
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Volume of cylinder = \(\pi\)r\(^2\)h = \(\pi\)a\(^2\)y
Volume of cone = \(\frac{1}{3}\) \(\pi\)r\(^2\)h = \(\frac{1}{3}\) \(\pi\)a\(^2\)x
Total Volume = \(\pi\)a\(^2\)y + \(\frac{1}{3}\) \(\pi\)a\(^2\)x = \(\frac{3\pi a^2y + \pi a^2x}{3}\)
= \(\frac{\pi a^2}{3}(x + 3y)\)
Source: Myschool Past Questions Archive (Record #32982)