# Areas Quiz Set 003

### Question 1

What is the area of the largest square that can be drawn inside a circle of radius 4 m?

A

32 sq. m.

B

33 sq. m.

C

31 sq. m.

D

34 sq. m.

Soln.
Ans: a

If the radius of the circle is R, then the side of an inscribed square is \$√2 × R\$, so the area is 2 × R2 = 2 × 42 = 32 sq. m.

### Question 2

The length and breadth of a rectangular area are in the ratio 3 : 1. What is the length of the field if a car travelling at 20 km/h covers one round of the rectangle in 48 minutes?

A

6 km.

B

8 km.

C

4 km.

D

10 km.

Soln.
Ans: a

Let L = 3x and B = 1x. Perimeter = 2 × (3x + 1x) = speed × time = (20 × 48)/60 = 16 km. So x = 2, and L = 3x = 6 km.

### Question 3

The length of a square is increased by 4%, what is the % increase in area?

A

8.16%.

B

17%.

C

11%.

D

16.32%.

Soln.
Ans: a

If x% is the increase in length, then area increases by \$(2x + x^2/100)\$%. Putting x = 4, the increase is \$(2 × 4 + 4^2/100)\$% = 8.16%

### Question 4

A rectangular wire 18 × 11 is re-aligned into a rectangle 9 × 33. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%.

### Question 5

A rectangular wire 22 × 3 is re-aligned into a rectangle 11 × 9. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%.