Question

A circular picture is 8 inches in diameter.

Part A.
What is the area of the picture in square inches.
A. 4 square inches
B. 8 square inches
C. 16 square inches
D. 32 square inches

Part B.
A frame that is 2 inches wide surrounds the picture. What is the total area of the picture and the frame in square inches?
A. 4 square inches
B. 12 square inches
C. 36 square inches
D. 40 square inches

Answer 1

The correct answers aren't listed, but

Part A: The area of the picture is 16π in²

Part B: The area including the frame is 36π in²

Explanation:

Part A:

The formula for area if a circle is A = πr², where A is the area, r is the radius, and π is the constant pi.

You are given the diameter of the circle, which is twice the radius, so divide the diameter in half to get the radius.

r = 8/2 = 4, so the area of the picture is

A = π(4²)

A = 16π in²

Part B:

Including the frame, the new diameter is 12 inches. It adds two inches all around, so that's 2 inches on each side of the diameter (8 + 2 + 2 = 12)

The new radius is 12/6 = 6 inches,

The area of the picture and frame is

A = π(6²)

A = 36π in²

Answer 2

part a: 16 sq in./ part b: 36 sq in

Explanation:

part a: area= π*r² = π(d/2)² = π*(8/2)² =

π*4² = π*16 square inches

part b: d=8+4 = 12 r = d/2 = 6 in

Area = π*6²

=36π