Areas Quiz Set 001

Question 1

Two concentric circles of radii 19 and 11 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

240π sq. cm.

B

480π sq. m.

C

57600π sq. m.

D

120π sq. m.

Soln.
Ans: a

The required area is difference of the areas of the two circles. π(\$19^2 - 11^2\$) = 240π sq. cm.

Question 2

The length and breadth of a rectangular area are in the ratio 5 : 3. What is the length of the field if a car travelling at 12 km/h covers one round of the rectangle in 320 minutes?

A

20 km.

B

22 km.

C

18 km.

D

24 km.

Soln.
Ans: a

Let L = 5x and B = 3x. Perimeter = 2 × (5x + 3x) = speed × time = (12 × 320)/60 = 64 km. So x = 4, and L = 5x = 20 km.

Question 3

What is the area of the largest circle that can fit completely inside a square of side 14 meters?

A

49π sq. m.

B

98π sq. m.

C

2401π sq. m.

D

24.5π sq. m.

Soln.
Ans: a

The radius of such a circle is 14/2 = 7 m. So its area = π × 7 × 7 = 49π sq. m.

Question 4

A gun is fired towards a circular board consisting of two concentric circles of radii 12 and 3 cm. If each bullet is able to hit the board, what is the probability that it will strike the ring, i.e., the area between the inner and outer circles?

A

\${15/16}\$.

B

\${5/7}\$.

C

1/2.

D

\${15/31}\$.

Soln.
Ans: a

The area of the ring is equal to the difference of the areas of the two circles. π(\$12^2 - 3^2\$) = 135π sq. cm. The total area is π × 122 = 144π. The probability of hitting the ring is \${135π}/{144π}\$ = \${15/16}\$.

Question 5

A largest possible circle is cut out of a square sheet having a side of 18 meter. What is the area of the hollow sheet?

A

324 - 81π sq. m.

B

18 + 162π sq. m.

C

18 + 6561π sq. m.

D

324 - 40.5π sq. m.

Soln.
Ans: a

The radius of the circle is 18/2 = 9 m. So its area = π × 9 × 9 = 81π sq. m. The left area is \$18^2 - 81\$π = \$324 - 81\$π sq. m. This Blog Post/Article "Areas Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.