# Areas Quiz Set 014

### Question 1

A rectangular wire 22 × 10 is re-aligned into a rectangle 11 × 30. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%.

### Question 2

What is the area of the largest square that can be drawn inside a circle of radius 19 m?

A

722 sq. m.

B

723 sq. m.

C

721 sq. m.

D

724 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 × 192 = 722 sq. m.

### Question 3

A gun is fired towards a circular board consisting of two concentric circles of radii 19 and 13 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

\${192/361}\$.

B

\${32/61}\$.

C

1/2.

D

\${24/47}\$.

Soln.
Ans: a

The area of the ring is equal to the difference of the areas of the two circles. π(\$19^2 - 13^2\$) = 192π sq. cm. The total area is π × 192 = 361π. The probability of hitting the ring is \${192π}/{361π}\$ = \${192/361}\$.

### Question 4

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.

### Question 5

The diagonal and one side of a rectangle are 10 m and 8 m. What is the perimeter of the rectangle?

A

28 m.

B

30 m.

C

26 m.

D

32 m.

Soln.
Ans: a

The side = \$√{10^2 - 8^2}\$ = \$√{100 - 64}\$ = 6. So the perimeter = 2 × (8 + 6) = 28 m.

Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer