An architect's blueprint shows a circular courtyard with a diameter of 2 inches. The scale… — Armed Services Vocational Aptitude Battery (ASVAB)

An architect's blueprint shows a circular courtyard with a diameter of $2$ inches. The scale on the blueprint is $1 \text{ inch} = 6 \text{ yards}$ . What is the actual area of the courtyard in square yards? (Use $\pi = 3.14$ )

A
$11.304$
B
$18.84$
$113.04$ Answer
D
$452.16$

Answer

The actual area of the courtyard is

113.04

square yards.

First, the blueprint diameter of

2

inches must be converted to the actual diameter using the scale

1 \text{ inch} = 6 \text{ yards}

. This gives an actual diameter of

12

yards. Next, the radius is found by halving the diameter, resulting in

6

yards. Finally, applying the area formula

A = \pi \times r^2

, the calculation is

3.14 \times 6^2 = 3.14 \times 36 = 113.04

square yards.

Step-by-Step Solution

Use the scale to find the actual diameter of the courtyard.

2 \text{ inches} \times 6 \text{ yards/inch} = 12 \text{ yards}

Before calculating the actual area, the blueprint dimensions must be converted to actual dimensions.

Find the actual radius.

12 \text{ yards} \div 2 = 6 \text{ yards}

The area formula for a circle requires the radius, which is half of the diameter.

Calculate the area using the formula

A = \pi \times r^2

A = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \text{ square yards}

This determines the total two-dimensional space the courtyard will occupy.

Key Concept

Calculating circular area from a scale drawing requires converting the linear dimensions first, and ensuring the radius is used instead of the diameter in the formula

A = \pi r^2

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