# Areas Quiz Set 014

### 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

What is the length of the fence required if a square plot of area 324 sq. m. has to fenced on three sides?

A

54 meters.

B

56 meters.

C

52 meters.

D

58 meters.

Soln.
Ans: a

Area of a square is L2 = 324, which gives L = 18. If three sides have to be fenced, the required length = 3 × L = 3 × 18 = 54 m.

### Question 3

A largest possible circle is cut out of a square sheet having a side of 4 meter. What is the area of the hollow sheet?

A

16 - 4π sq. m.

B

4 + 8π sq. m.

C

4 + 16π sq. m.

D

16 - 2π sq. m.

Soln.
Ans: a

The radius of the circle is 4/2 = 2 m. So its area = π × 2 × 2 = 4π sq. m. The left area is \$4^2 - 4\$π = \$16 - 4\$π sq. m.

### Question 4

Three squares have their sides such that they are in an AP(Arithmetic Progression). If the side of the middle square is 4, what is the area of the square whose side is equal to the sum of the sides of these three squares?

A

144 sq. units.

B

148 sq. units.

C

140 sq. units.

D

152 sq. units.

Soln.
Ans: a

Let the sides of the three squares be 4 - d, 4 and 4 + d, where d is the common difference. The sum of these is 12, and the area would be \$12^2\$ = 144 sq. units.

### Question 5

A largest possible circle is cut out of a square sheet having a side of 8 meter. What is the area of the hollow sheet?

A

64 - 16π sq. m.

B

8 + 32π sq. m.

C

8 + 256π sq. m.

D

64 - 8π sq. m.

Soln.
Ans: a

The radius of the circle is 8/2 = 4 m. So its area = π × 4 × 4 = 16π sq. m. The left area is \$8^2 - 16\$π = \$64 - 16\$π sq. m. 