Question

In order to calculate the heat loss of this restaurant, Kevin needs to find the area of the surface that is exposed to air. ABC is a semi-circle. Round the answer to three significant figures.​

Answer 1

The area of the surface that is exposed to air. ABC is a semi-circle is equal to 1998.73 squared feet.

In Mathematics and Geometry, the area of a semicircle can be calculated by using this mathematical equation (formula):

Area of semicircle = 1/2 × π
`r^2`

Where:

d represents the diameter of a circle.

For the area of a quadrant, we have;

Area of quadrant = 1/4 × π
`r^2`

For the area of a rectangle, we have;

Area of quadrant = length × breadth

Based on the diagram, the area of the surface (composite figure) that is exposed to air can be calculated as follows;

Area of surface = 2(1/2 × π ×
`10^2`) + (1/2 × π × 2 × 10 × 20) + (20 × 10) + 2(1/4 × π ×
`7^2`) + (1/4 × π × 2 × 7 × 20) + 2(7 × 30) + (20 × 7).

Area of surface = 100π + 200π + 200 + 49π/2 + 70π + 420 + 140

Area of surface = 314 + 628 + 200 + 76.93 + 219.8 + 560

Area of surface = 1998.73 squared feet.