# Areas Quiz Set 010

### Question 1

Two concentric circles of radii 11 and 4 cm are drawn on a paper. What is the area of the portion that is inside the outer circle but outside the inner circle?

A

105π sq. cm.

B

210π sq. m.

C

11025π sq. m.

D

52π sq. m.

Soln.
Ans: a

The required area is difference of the areas of the two circles. π(\$11^2 - 4^2\$) = 105π sq. cm.

### Question 2

What is the area of the largest circle that can fit completely inside a square of side 6 meters?

A

9π sq. m.

B

18π sq. m.

C

81π sq. m.

D

4.5π sq. m.

Soln.
Ans: a

The radius of such a circle is 6/2 = 3 m. So its area = π × 3 × 3 = 9π sq. m.

### Question 3

The length and breadth of a rectangle are in the ratio 13 : 2. What is the perimeter if the area is 104 sq. meters?

A

60 meters.

B

62 meters.

C

58 meters.

D

64 meters.

Soln.
Ans: a

Let L = 13x and B = 2x. We are given (13x × 2x) = 104, which gives x = 2. So perimeter = 2 × ((13 × 2) + (2 × 2)) × = 60 meters.

### Question 4

The length and breadth of a rectangle are in the ratio 19 : 7. What is the perimeter if the area is 2128 sq. meters?

A

208 meters.

B

210 meters.

C

206 meters.

D

212 meters.

Soln.
Ans: a

Let L = 19x and B = 7x. We are given (19x × 7x) = 2128, which gives x = 4. So perimeter = 2 × ((19 × 4) + (7 × 4)) × = 208 meters.

### Question 5

The length and breadth of a rectangle are respectively increased by 7% and 4%. What is the % increase in the area?

A

\$11{7/25}\$%.

B

\$12{19/24}\$%.

C

\$9{14/27}\$%.

D

\$13{2/9}\$%.

Soln.
Ans: a

If x% and y% is the increase in the dimensions, then the area of a rectangle increases by \$(x + y + {xy}/100)\$% = \$(7 + 4 + {7 × 4}/100)\$% = \${282/25}\$, which is same as: \$11{7/25}\$%