Scale Drawings and Circles

1. The scale is:

$1 inch = 8 feet$

The drawing length is 3.5 inches:

$3.5 \times 8 = 28$

The actual room length is 28 feet.

2. First find the kilometers represented by 1 centimeter:

$15 \div 2 = 7.5$

So 1 centimeter represents 7.5 kilometers.

Now multiply by 9 centimeters:

$9 \times 7.5 = 67.5$

The actual distance is 67.5 kilometers.

3. a) Diameter is twice the radius:

$d = 2r$

$d = 2 \times 6 = 12$

The diameter is 12 meters.

b) Circumference:

$C = \pi \times d$

$C = 3.14 \times 12 = 37.68$

The circumference is 37.68 meters.

c) Area:

$A = \pi \times r^2$

$A = 3.14 \times 6^2$

$A = 3.14 \times 36 = 113.04$

The area is 113.04 square meters.

4. Use the circumference formula:

$C = \pi \times d$

Substitute $\pi = 22/7$ and $d = 28$:

$C = 22/7 \times 28$

$28 \div 7 = 4$

$C = 22 \times 4 = 88$

The circumference is 88 inches.

5. a) Use the scale 1 inch represents 25 feet.

Length:

$6 \times 25 = 150$

Width:

$4 \times 25 = 100$

The actual dimensions are 150 feet by 100 feet.

b) Area:

$A = 150 \times 100 = 15,000$

The actual area is 15,000 square feet.