Areas Quiz Set 015

Question 1

A gun is fired towards a circular board consisting of two concentric circles of radii 8 and 2 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(\$8^2 - 2^2\$) = 60π sq. cm. The total area is π × 82 = 64π. The probability of hitting the ring is \${60π}/{64π}\$ = \${15/16}\$.

Question 2

The difference between the length and breadth of a rectangle is 6 m. What is the area if the perimeter is 20 meters?

A

16 sq. meters.

B

18 sq. meters.

C

14 sq. meters.

D

20 sq. meters.

Soln.
Ans: a

If L and B are the length and breadth of the rectangle, then L - B = 6 and 2(L + B) = 20. Solving, we get L = 8 and B = 2, so the area is 8 × 2 = 16 sq. m. TIP: Sometimes long multiplications can be avoided by looking at the units place of the given options.

Question 3

What is the ratio of the perimeter of a circle of radius 4 units to that of a square having the circle's diameter as its side?

A

π : 4.

B

π : 2.

C

4 : 3.

D

4 : 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 4

What is the smallest number of square tiles that can be laid fully, without cutting, on a floor 36 m by 34 m?

A

306 .

B

307 .

C

305 .

D

308 .

Soln.
Ans: a

The side of the square tile has to be HCF(36, 34) = 2. Hence, the required number is \${36 × 34}/{2 × 2}\$ = 306.

Question 5

What is the area of the largest square that can be drawn inside a circle of radius 18 m?

A

648 sq. m.

B

649 sq. m.

C

647 sq. m.

D

650 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 × 182 = 648 sq. m.