Perimeter and Area — Measuring Space — Practice

Question 1

Find the perimeter of a rectangle 8 cm by 5 cm.

Accepted Answer

Step 1 — P = 2(l + b) = 2(8 + 5).

Step 2 — = 2 × 13 = 26 cm.

✦ Answer: 26 cm.

Question 2

Find the circumference of a circle of radius 7 cm. (π = 22/7)

Accepted Answer

Step 1 — C = 2πr = 2 × 22/7 × 7.

Step 2 — = 44 cm.

✦ Answer: 44 cm.

Question 3

What does the ratio of a circle's circumference to its diameter equal?

Accepted Answer

It equals π (the same for every circle), about 3.14159.

✦ Answer: π.

Question 4

Find the area of a circle whose diameter is 28 cm. (π = 22/7)

Accepted Answer

Step 1 — r = 28/2 = 14 cm.

Step 2 — A = πr² = 22/7 × 14 × 14 = 22 × 28 = 616 cm².

✦ Answer: 616 cm².

Question 5

The circumference of a circle is 88 cm. Find its radius. (π = 22/7)

Accepted Answer

Step 1 — C = 2πr → 88 = 2 × 22/7 × r.

Step 2 — r = (88 × 7)/(2 × 22) = 616/44 = 14 cm.

✦ Answer: 14 cm.

Question 6

Find the length of an arc subtending 60° at the centre of a circle of radius 21 cm. (π = 22/7)

Accepted Answer

Step 1 — arc = (60/360) × 2πr = (1/6) × 2 × 22/7 × 21.

Step 2 — = (1/6) × 132 = 22 cm.

✦ Answer: 22 cm.

Question 7

A sector has central angle 90° in a circle of radius 14 cm. Find its perimeter. (π = 22/7)

Accepted Answer

Step 1 — arc = (90/360) × 2 × 22/7 × 14 = (1/4) × 88 = 22 cm.

Step 2 — perimeter = arc + 2r = 22 + 28 = 50 cm.

✦ Answer: 50 cm.

Question 8

Find the area of a sector of angle 72° in a circle of radius 10 cm. (π = 3.14)

Accepted Answer

Step 1 — A = (θ/360) × πr² = (72/360) × 3.14 × 10².

Step 2 — = (1/5) × 3.14 × 100 = (1/5) × 314 = 62.8 cm².

✦ Answer: 62.8 cm².

Practice — Perimeter and Area — Measuring Space