MCQ on Area and Perimeter | Page 4 of 4 | for Competitive Exams

Area and Perimeter for SSC

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5 persons will live in a tent. If each person requires 16m2 of floor area and 100 m3 space for air then the height of the cone of smallest size to accommodate these persons would be?

(a) 18.75 m

(b) 16 m

(d) 20 m

(e) None of these

Solution: (a)

For surface Area of 5 person

\(\displaystyle \pi {{r}^{2}}=5\times 16\)

\(\displaystyle {{r}^{2}}=\frac{{80}}{\pi }\)

Now, volume of cone = volume of air space of 5 person

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{1}{3}\pi {{r}^{2}}h=5\times 100\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{1}{3}\pi \times \frac{{80}}{{\pi h}}=5\times 100\)

\(\displaystyle h=\frac{{75}}{4}=18.75\)

An ice-cream company makes a popular brand of ice-cream in rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut the cost, the company has decided to reduce the volume of the bar by 20%, the thickness remaining the same, but the length and width will be decreased by the same percentage amount. The new length L will satisfy :

(a) \(\displaystyle 5.5<L<6\)

(b) \(\displaystyle 5<L<5.5\)

(d) \(\displaystyle 4<L<4.5\)

(e) None of these

Solution: (b)

\(\displaystyle L\times B\times 2=48\)

\(\displaystyle L\times B=24\)

Now, \(\displaystyle 6-6\times 10\%=5.4\)

\(\displaystyle 5-5\times 10\%=4.5\)and

Therefore, \(\displaystyle 5.4\times 4.5=24.3\)

Clearly, \(\displaystyle 5<L<5.5\)

The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) remain the same

(b) decrease by 13.64%

(d) decrease by 18.75%

(e) decrease by 30%

Solution: (e)

Total area of four walls of a room = 2h(l + b)

Let the height of the room be x.

The breadth = 2x and length = 3x

\(\displaystyle Are{{a}_{{(1)}}}=2x(2x+3x)=10{{x}^{2}}\)

\(\displaystyle Are{{a}_{{(2)}}}=2\times \frac{x}{2}(\frac{{2x}}{2}+3x\times 2)=7{{x}^{2}}\)

Area of 4 walls decreases by 30%.

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is

(a) 3 : 1

(b) 13 : 9

(d) 34 : 9

(e) None of these

Solution: (c)

Let the radius of the base are 5k and 12k respectively

\(\displaystyle \frac{{totalsurfaceareaofcylinder}}{{totalsurfaceareaofthecone}}\)

\(\displaystyle \frac{{2\pi r\times h+2\pi {{r}^{2}}}}{{\pi r\sqrt{{{{r}^{2}}+{{h}^{2}}}}+\pi r}}\)

\(\displaystyle \frac{{2h+2r}}{{\sqrt{{{{r}^{2}}+{{h}^{2}}}}+r}}+\frac{{24k+10k}}{{\sqrt{{25{{k}^{2}}+144{{k}^{2}}}}+5k}}\)

\(\displaystyle \frac{{34k}}{{13k+5k}}=\frac{{34k}}{{18k}}=\frac{{17}}{9}or17:9\)

The area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot. What will be the length of the diagonal of the square plot?

(a) 120 m

(b) 100 m

(d) 105 m

(e) None of these

Solution: (a)

Given that the length of the rectangular field l = 90 m and breadth b = 80 m.

Then its area lb = \(\displaystyle 90\times 80\) sq.m

We know that the area of square = \(\displaystyle (\frac{1}{2})\times {{(diagonal)}^{2}}\)

from the given question, we have area of square plot = area of rectangular field

That is, \(\displaystyle 90\times 80\)= \(\displaystyle \frac{1}{2}\times diagona{{l}^{2}}\)

\(\displaystyle diagona{{l}^{2}}=2\times 7200=14400={{120}^{2}}\)

diagonal = 120 m.

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Area and Perimeter for SSC

5 persons will live in a tent. If each person requires 16m2 of floor area and 100 m3 space for air then the height of the cone of smallest size to accommodate these persons would be?

The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is

The area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot. What will be the length of the diagonal of the square plot?

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