The diameter of the base of the cylinder is 8 and the volume is 64π. 1) Find the surface area of the base of the cylinder. 2) Find the height of the cylinder. 3) Find the area of the lateral surface of the cylinder.

Given diameter \( d = 8 \), so radius \( r = 4 \). Volume \( V = \pi r^2 h = 64\pi \).

1) Area of base: \( S_{\text{base}} = \pi r^2 = \pi \cdot 4^2 = 16\pi \).

2) Height: \( \pi \cdot 16 \cdot h = 64\pi \Rightarrow 16h = 64 \Rightarrow h = 4 \).

3) Lateral surface area: \( S_{\text{lateral}} = 2\pi r h = 2\pi \cdot 4 \cdot 4 = 32\pi \).

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