Question

A circular pie with radius 8.5 cm is served on a square plate with sides 21 cm long. What proportion of the area of the plate does the pie cover?

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Answer 1

`Proportion = 51.49`%

Step-by-step explanation:

Given

Radius of Circular Pie = 8.5 cm

Length of Square Plate = 21cm

Required:

Proportion of the area of the plate covered by the pie

To solve this, we simply calculate the area of the plate and area of the pie.

The area of the plate is calculated as area of a square;

`Area = Length^2`

`Area = (21cm)^2\\Area = 21cm * 21cm`

`Area = 441cm^2`

The area of the pie is calculated as area of a circle;

`Area = \pi r^2`

`Area = (22)/(7) * 8.5^2`

`Area = (22)/(7) * 8.5 * 8.5`

`Area = (1589.5)/(7)`

`Area = 227.1cm^2`

The proportion covered by the pie is then calculated as thus;

Proportion = Area of Pie / Area of Plate

`Proportion = (227.1cm^2)/(441cm^2)`

`Proportion = 0.5149` (Approximated)

Convert to percent

`Proportion = 0.5149 * 100`%

`Proportion = 51.49`%

Hence, the proportion covered by the pie is 51.49%