Question

d = 30, 34 (a cone diagram with diameter d = 30 and height 34)

Explanation:

Step1: Find the radius of the base

The diameter \( d = 30 \), so the radius \( r=\frac{d}{2}=\frac{30}{2} = 15 \).

Step2: Recall the volume formula for a cone

The volume \( V \) of a cone is given by \( V=\frac{1}{3}\pi r^{2}h \), where \( h = 34 \) (height of the cone) and \( r = 15 \) (radius of the base).

Step3: Substitute the values into the formula

\( V=\frac{1}{3}\times\pi\times15^{2}\times34 \)
First, calculate \( 15^{2}=225 \).
Then, \( \frac{1}{3}\times225 = 75 \).
So, \( V=75\times34\times\pi=2550\pi \) (If we take \( \pi\approx3.14 \), then \( V\approx2550\times3.14 = 8007 \)).

Answer:

If we leave it in terms of \( \pi \), the volume is \( 2550\pi \); if we use \( \pi\approx3.14 \), the volume is approximately \( 8007 \).