Areas Quiz Set 005

Question 1

A largest possible circle is cut out of a square sheet having a side of 12 meter. What is the area of the hollow sheet?

A

144 - 36π sq. m.

B

12 + 72π sq. m.

C

12 + 1296π sq. m.

D

144 - 18π sq. m.

Soln.
Ans: a

The radius of the circle is 12/2 = 6 m. So its area = π × 6 × 6 = 36π sq. m. The left area is \$12^2 - 36\$π = \$144 - 36\$π sq. m.

Question 2

The length and breadth of a rectangle are in the ratio 13 : 6. What is the area if the perimeter is 266 meters?

A

3822 sq. meters.

B

3824 sq. meters.

C

3820 sq. meters.

D

3826 sq. meters.

Soln.
Ans: a

Let L = 13x and B = 6x. We are given 2 × (13x + 6x) = 266, which gives x = 7. So area = L × B = (13 × 7) × (6 × 7) = 3822 sq. meters.

Question 3

The length and breadth of a rectangle are respectively increased by 4% and 1%. What is the % increase in the area?

A

\$5{1/25}\$%.

B

\$6{7/24}\$%.

C

\$3{20/27}\$%.

D

\$7{4/9}\$%.

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)\$% = \$(4 + 1 + {4 × 1}/100)\$% = \${126/25}\$, which is same as: \$5{1/25}\$%

Question 4

What is the length of the fence required if a square plot of area 484 sq. m. has to fenced on three sides?

A

66 meters.

B

68 meters.

C

64 meters.

D

70 meters.

Soln.
Ans: a

Area of a square is L2 = 484, which gives L = 22. If three sides have to be fenced, the required length = 3 × L = 3 × 22 = 66 m.

Question 5

What is the cost of plastering, @50 paise per square meter, the walls and floor of a 8 m × 2 m. tank that is 36 meters high?

A

Rs. 368 .

B

Rs. 370 .

C

Rs. 366 .

D

Rs. 372 .

Soln.
Ans: a

The area to be plastered is \$(2 × l × h) + (2 × b × h) + (l × b)\$ = (2 × 8 × 36) + (2 × 2 × 36) + (8 × 2) = 736 sq. m. The cost = 736 × 0.50 = Rs. 368. This Blog Post/Article "Areas Quiz Set 005" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.