Question

What is the lateral area of a cylinder with a base radius length of 4 inches and a height of 7 inches? Round to the nearest hundredth.

(1 point)
Responses

351.86 square inches
351.86 square inches

100.53 square inches
100.53 square inches

226.19 square inches
226.19 square inches

175.93 square inches
175.93 square inches

Answer 1

The lateral area \( A \) of a cylinder can be calculated using the formula:

\[
A = 2 \pi r h
\]

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

Given:
- Radius \( r = 4 \) inches,
- Height \( h = 7 \) inches.

Now, substituting the values into the formula:

\[
A = 2 \pi (4)(7)
\]

Calculating that:

\[
A = 2 \pi (28) = 56 \pi
\]

To find the numerical value, we can use \( \pi \approx 3.14 \):

\[
56 \pi \approx 56 \times 3.14 = 175.84
\]

Rounding to the nearest hundredth, we get:

\[
A \approx 175.84 \text{ square inches}
\]

However, it looks like we may have misstated the available options in the summary.

Thus, the closest option to 175.84 square inches would be:
- **175.93 square inches**

(It's important to note the slight discrepancy due to rounding \( \pi \)).