Question

example 1.) determine the surface area.

radius =
surface area:

you try! 2.) determine the surface area.

radius =
surface area:

Explanation:

Example 1:

Step 1: Find the radius

The diameter is 24 yd, so the radius \( r=\frac{24}{2}=12 \) yd. The height (length) of the cylinder - like shape (maybe a cylinder with some parts, but from the diagram, the curved length is 6 yd? Wait, no, maybe it's a cylinder? Wait, the surface area of a cylinder is \( 2\pi r^2 + 2\pi rh \), but maybe this is a different shape. Wait, the diagram shows two circular faces and a curved surface. Wait, the given length is 6 yd. Wait, maybe it's a cylinder with radius \( r = 12 \) yd and height \( h=6 \) yd?
Wait, let's re - examine. The diameter is 24 yd, so radius \( r = 12 \) yd. The surface area of a cylinder is \( S=2\pi r^2+2\pi rh \). If \( h = 6 \) yd.

Step 2: Calculate the surface area

First, calculate the area of the two circular faces: \( 2\pi r^2=2\times\pi\times12^2 = 2\times\pi\times144 = 288\pi \)
Then, calculate the lateral (curved) surface area: \( 2\pi rh=2\times\pi\times12\times6 = 144\pi \)
Total surface area \( S=288\pi + 144\pi=432\pi\approx432\times3.14 = 1356.48 \) square yards. But wait, maybe the shape is different. Wait, the diagram has a length of 6 yd and diameter 24 yd. Alternatively, maybe it's a cylinder with radius \( r = 12 \) yd and height \( h = 6 \) yd. So radius \( r = 12 \) yd, surface area \( S = 2\pi r(r + h)=2\pi\times12\times(12 + 6)=2\pi\times12\times18 = 432\pi\approx1356.48 \) square yards.

You Try! 2:

Step 1: Identify the radius and height

The radius \( r = 3 \) yd and the height \( h=9 \) yd.

Step 2: Use the formula for the surface area of a cylinder

The formula for the surface area of a cylinder is \( S = 2\pi r^2+2\pi rh \)
First, calculate the area of the two circular bases: \( 2\pi r^2=2\times\pi\times3^2=2\times\pi\times9 = 18\pi \)
Then, calculate the lateral surface area: \( 2\pi rh=2\times\pi\times3\times9 = 54\pi \)

Step 3: Sum the two areas

Total surface area \( S=18\pi + 54\pi=72\pi\approx72\times3.14 = 226.08 \) square yards.

Example 1 Answers:

Radius: \( 12 \) yd
Surface Area: \( 432\pi\approx1356.48 \) square yards (or \( 432\pi \) square yards)

You Try! 2 Answers:

Radius: \( 3 \) yd
Surface Area: \( 72\pi\approx226.08 \) square yards (or \( 72\pi \) square yards)

Answer:

Step 1: Identify the radius and height

The radius \( r = 3 \) yd and the height \( h=9 \) yd.

Step 2: Use the formula for the surface area of a cylinder

The formula for the surface area of a cylinder is \( S = 2\pi r^2+2\pi rh \)
First, calculate the area of the two circular bases: \( 2\pi r^2=2\times\pi\times3^2=2\times\pi\times9 = 18\pi \)
Then, calculate the lateral surface area: \( 2\pi rh=2\times\pi\times3\times9 = 54\pi \)

Step 3: Sum the two areas

Total surface area \( S=18\pi + 54\pi=72\pi\approx72\times3.14 = 226.08 \) square yards.

Example 1 Answers:

Radius: \( 12 \) yd
Surface Area: \( 432\pi\approx1356.48 \) square yards (or \( 432\pi \) square yards)

You Try! 2 Answers:

Radius: \( 3 \) yd
Surface Area: \( 72\pi\approx226.08 \) square yards (or \( 72\pi \) square yards)