Question

A bakery offers a small circular cake with a diameter of 8 inches it also offers a large circular cake with a diameter of 24 inches does the top of the large cake have three times the area of the small cake

Answer 1

• The area of the small cake is 144π in 2.

• The area of the large cake is 16π 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(4)2 Substitute. Use 4 for r.

A = π × 16 Evaluate the power.

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

A = πr2 Use the formula.

A = π(12)2 Substitute. Use 12 for r.

A = π × 144 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.

144π ÷ 16π = 9

Answer 2

Answer: No, the larger cake's area is greater than 3 times the area of the small cake.

Explanation:

Area of a circle =
`\pi`r^2

small cake: diameter = 8, so radius = 4

area = 16pi

large cake: diameter = 24, radius = 12

area = 144pi