Question

A bakery offers a small circular cake with a diameter of 6 inches. It also offers a large circular cake with a diameter of 18 inches. Complete the explanation for wether the top of the large cake has three times the area that of the small cake.

The area of the top of the large cake is ____ pie in2 and that of the small cake is ______ pie in2. The top of the cake has an area equal to _____ times that of the small cake.

Answer 1

• The area of the small cake is 81π in 2.

• The area of the large cake is 9π in2.

• The top of the large cake has an area equal to 9 times that of the small cake.

Explanation:

Find the area of the small cake in terms of π.

A = πr2 Use the formula.

A = π(3)2 Substitute. Use 3 for r.

A = π × 9 Evaluate the power.

Find the area of the top of the large cake in terms of π.

A = πr2 Use the formula.

A = π(9)2 Substitute. Use 9 for r.

A = π × 81 Evaluate the power.

Find how much larger the area of the top of the large cake is compared to the area of the small cake.

81π ÷ 9π = 9

Answer 2

The area of the top of the large cake is 254.34 in2 and the small cake is 28.26 in2. The top of the large cake has an area equal to 9 times that of the small cake.

Explanation:

Area of a circle is TTr^2 (TT is pi).

Large cake: 3.14x9^2=254.34

Small cake: 3.14x3^2=28.26

254.34/28.26=9