Question

1. a circle with a radius of 32 cm (diagram shows a circle with its center and a radius labeled 32 cm)

Explanation:

Assuming the problem is to find the area or circumference of the circle with radius \( r = 32 \, \text{cm} \). Let's solve for the area first (common problem with circles).

Step 1: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle is \( A = \pi r^2 \), where \( r \) is the radius.

Step 2: Substitute the given radius into the formula

Given \( r = 32 \, \text{cm} \), substitute into the formula:
\( A = \pi (32)^2 \)

Step 3: Calculate \( 32^2 \)

\( 32^2 = 32 \times 32 = 1024 \)

Step 4: Multiply by \( \pi \)

\( A = \pi \times 1024 = 1024\pi \, \text{cm}^2 \) (or approximately \( 1024 \times 3.14 = 3215.36 \, \text{cm}^2 \))

If the problem was about circumference, the formula is \( C = 2\pi r \):

Step 1: Recall the formula for circumference

\( C = 2\pi r \)

Step 2: Substitute \( r = 32 \)

\( C = 2\pi \times 32 = 64\pi \, \text{cm} \) (or approximately \( 64 \times 3.14 = 200.96 \, \text{cm} \))

Since the problem wasn't specified, but the radius is given, let's assume area (more common for a shaded circle).

Answer:

If area: \( 1024\pi \, \text{cm}^2 \) (or \( 3215.36 \, \text{cm}^2 \))
If circumference: \( 64\pi \, \text{cm} \) (or \( 200.96 \, \text{cm} \))

(Assuming area is required, the answer is \( 1024\pi \, \text{cm}^2 \) or approximately \( 3215.36 \, \text{cm}^2 \))