Question

a cylinder has a height of 4 yards and a radius of 4 yards. what is its volume? round your answer to the nearest hundredth. 200.96 401.92 803.84 535.89 26 in 11 in 5,837.26 2918.63 1459.32 729.66

Explanation:

First Question (Cylinder with height 4 yd, radius 4 yd)

Step1: Recall cylinder volume formula

The formula for the volume \( V \) of a cylinder is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute values

Given \( r = 4 \) yards and \( h = 4 \) yards. Substitute into the formula: \( V=\pi\times(4)^2\times4 \).

Step3: Calculate

First, \( 4^2 = 16 \). Then, \( 16\times4 = 64 \). So \( V = \pi\times64 \approx 3.14159\times64 \approx 200.96 \) (rounded to the nearest hundredth).

Second Question (Cylinder with diameter 26 in, height 11 in)

Step1: Find radius from diameter

The diameter is 26 in, so radius \( r=\frac{26}{2}=13 \) in.

Step2: Use cylinder volume formula

Volume \( V = \pi r^2 h \), with \( r = 13 \) in and \( h = 11 \) in. Substitute: \( V=\pi\times(13)^2\times11 \).

Step3: Calculate

\( 13^2 = 169 \), \( 169\times11 = 1859 \). Then \( V=\pi\times1859 \approx 3.14159\times1859 \approx 5837.26 \) (rounded to the nearest hundredth).

Answer:

First Question: 200.96
Second Question: 5,837.26