volume_mute

Volume of a Cylinder (d = 10 yd, h = 4 yd)

publish date: 2026/05/18 20:42:22.242551 UTC

volume_mute

Find the volume of the cylinder shown below. Give the exact answer and an approximation to the nearest hundredth.

Exact: \(40\pi\) yd³ Approx: ≈ 125.66 yd³

Exact: \(80\pi\) yd³ Approx: ≈ 251.33 yd³

Exact: \(100\pi\) yd³ Approx: ≈ 314.16 yd³

Exact: \(400\pi\) yd³ Approx: ≈ 1,256.64 yd³

Exact: \(100\pi\) yd³ Approx: ≈ 314.16 yd³

Since the diameter is 10 yards, the radius is \(r = \frac{10}{2} = 5\) yd. The height is 4 yd.

\[V = \pi r^2 h\]

This is the formula for the volume of a cylinder.

\[V = \pi(5)^2(4)\]

Substitute 5 for \(r\) and 4 for \(h\).

\[= \pi(25)(4)\]

Evaluate the exponential expression: \((5)^2 = 25\).

\[= 100\pi \approx 314.16 \text{ yd}^3\]

The exact volume is \(100\pi\) yd³. To the nearest hundredth, the volume is 314.16 yd³.

Mathematics for college students