Areas Quiz Set 006

Question 1

What is the ratio of the perimeter of a circle of radius 12 units to that of a square having the circle's diameter as its side?

A

π : 4.

B

π : 2.

C

12 : 3.

D

12 : π.

Soln.
Ans: a

Let X be the radius of the circle, so the side of the square is 2X. The ratio of the perimeters = \${2 × π × X}/{4 × (2X)}\$ = π/4.

Question 2

What is the cost of plastering, @50 paise per square meter, the walls and floor of a 26 m × 6 m. tank that is 8 meters high?

A

Rs. 334 .

B

Rs. 336 .

C

Rs. 332 .

D

Rs. 338 .

Soln.
Ans: a

The area to be plastered is \$(2 × l × h) + (2 × b × h) + (l × b)\$ = (2 × 26 × 8) + (2 × 6 × 8) + (26 × 6) = 668 sq. m. The cost = 668 × 0.50 = Rs. 334.

Question 3

Two concentric circles of radii 14 and 7 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

147π sq. cm.

B

294π sq. m.

C

21609π sq. m.

D

73π sq. m.

Soln.
Ans: a

The required area is difference of the areas of the two circles. π(\$14^2 - 7^2\$) = 147π sq. cm.

Question 4

The length and breadth of a rectangular area are in the ratio 9 : 7. What is the length of the field if a car travelling at 15 km/h covers one round of the rectangle in 384 minutes?

A

27 km.

B

29 km.

C

25 km.

D

31 km.

Soln.
Ans: a

Let L = 9x and B = 7x. Perimeter = 2 × (9x + 7x) = speed × time = (15 × 384)/60 = 96 km. So x = 3, and L = 9x = 27 km.

Question 5

The diagonal and one side of a rectangle are 29 m and 21 m. What is the perimeter of the rectangle?

A

82 m.

B

84 m.

C

80 m.

D

86 m.

Soln.
Ans: a

The side = \$√{29^2 - 21^2}\$ = \$√{841 - 441}\$ = 20. So the perimeter = 2 × (21 + 20) = 82 m.