# Mensuration Questions for SSC CHSL PDF

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## Mensuration Questions for SSC CHSL PDF:

SSC CHSL Mensuration Questions download PDF based on previous year question paper of SSC CHSL exam. 25 Very important Mensuration questions for SSC CHSL Exam.

SSC CHSL Study Material (FREE Tests) Question 1: The edge of an ice cube is 14 cm. The volume of the largest cylindrical ice cube that can be formed out of it is

a) 2200 cu. cm

b) 2000 cu. cm

c) 2156 cu. cm

d) 2400 cu. cm

e) None of these

Question 2: A rope makes 125 rounds of a cylinder with base radius 15 cm. How many times can it go round a cylinder with base radius 25 cm?

a) 100

b) 75

c) 80

d) 65

e) None of these

Question 3: What is the area of the triangle whose vertices are (0,0), (5,0) and (0,6)?

a) 30 sq units

b) 15 sq units

c) 20 sq units

d) 10 sq units

e) None of the above

Question 4: A rectangular field of dimensions 30 m x 20 m is surrounded by a footpath of uniform width. If the area of the footpath is 216 $m^2$, what is the width of the footpath?

a) 2 m

b) 3 m

c) 1 m

d) 2.5 m

e) None of the above

Question 5: Which of the following cannot be the ratio of angles of a right-angled triangle?

a) 1:2:3

b) 1:1:2

c) 5:6:7

d) 1:5:6

e) None of the above

Question 6: In a triangle ABC, a line is drawn parallel to BC such that it cuts AB at D and AC at E. If DE/BC = ½, what is the ratio of the area of triangle ABC to the area of the triangle ADE?

a) 4:1

b) 1:4

c) 2:1

d) 1:2

e) None of the above

Question 7: The sides of a right-angled triangle are in Arithmetic Progression. If the length of the largest side is 10 cm, what is the area of the triangle?

a) 48 $cm^2$

b) 60 $cm^2$

c) 72 $cm^2$

d) 24 $cm^2$

e) None of the above

Question 8: The length of a rectangle is increased by 25% and the breadth of the rectangle is decreased by 25%. What is the percentage change in the area of the rectangle?

a) 5% decrease

b) 5% increase

c) 6.25% increase

d) 6.25% decrease

e) None of the above

Question 9: The length of a rectangle is increased by 25% and the breadth of the rectangle is decreased by 25%. What is the percentage change in its perimeter?

a) 5% increase

b) 5% decrease

c) 10% increase

d) 10% decrease

e) Can’t be determined

Question 10: A triangle ABC has lengths AB = 10 cm, BC = 9 cm and CA = 8 cm. What is the length of the median BD?

a) $\sqrt{74.5}$

b) $\sqrt{84.5}$

c) $\sqrt{64.5}$

d) $\sqrt{54.5}$

e) $\sqrt{94.5}$ Question 11: The area of a square is 100 sq. cms. What is the approximate length of the diagonal?

a) 10

b) 14.1

c) 17.5

d) 20

e) 25

Question 12: The length of the side of a square is equal to the radius of a circle. If the area of the square is 100 sq metres, what is the area of the circle?

a) 314 sq metres

b) 414 sq metres

c) 514 sq metres

d) 614 sq metres

e) None of the above.

Question 13: The area of a square is the same as that of a circle. What is the ratio of the side of the square to the radius of the circle?

a) 1:pi

b) 1: sq.root pi

c) sq.root pi : 1

d) pi square : 1

e) None of the above

Question 14: In a right angled triangle, two sides are of the same length. Which of the options is one of the angles of that triangle?

a) 30

b) 45

c) 60

d) 75

e) None of the above

Question 15: The length of a rectangle is twice its breadth. If the area of the rectangle is 50 metre square, what is the length of the rectangle?

a) 5 metres

b) 10 metres

c) 25 metres

d) 50 metres

e) None of the above

Question 16: The length of a rectangle is 24 metres and its perimeter is 84 metres. Find the area of a triangle whose base is equal to the breadth of the rectangle and height equal to the rectangle’s diagonal?

a) 200

b) 210

c) 240

d) 270

e) None of the above

Question 17: The circumference of a circle is 100 $\pi$ metres. Find its area?

a) 2500 $\pi$

b) 3000 $\pi$

c) 3500 $\pi$

d) 3600 $\pi$

e) None of the above

Question 18: If the radius of a circle is equal to the side of a square, what is the ratio of the perimeters of the circle to the square?

a) $\pi$:1

b) $\pi$:2

c) $\pi$:3

d) 2:$\pi$

e) None of the above

Question 19: In a right angled traingle, two of the sides are of equal length. Which of the following is certainly one of the angles in the triangle?

a) 30

b) 45

c) 60

d) 75

e) Can’t be determined

Question 20: The length of a rectangle is thrice it’s breadth. The perimeter of the rectangle is 544 metres.
What is it’s area?

a) 18372

b) 23872

c) 13872

d) Can’t be determined

e) None of the above Question 21: If the diameter of a circle is equal to the diagonal of a square of area 100 sq. cms, what is the area of the circle?

a) 25 $\pi$

b) 50 $\pi$

c) 75 $\pi$

d) 100 $\pi$

e) None of the above

Question 22: In a regular polygon, the number of diagonals is 3 more than the number of sides. What is the number of sides of the polygon?

a) 3

b) 4

c) 5

d) 6

e) 7

Question 23: If the height of a hollow cylinder is increased by 25%, what will be the ratio its new area to its area before increment in height?

a) 5:4

b) 5:3

c) 6:5

d) 7:3

e) 4:7

Question 24: If radius of a circle is increased by 66.66%, then what will be percentage increment in the area of circle?

a) 200

b) 188.88

c) 199.99

d) 177.76

e) 162.22

Question 25: If length of a rectangle is increased by 10% and breadth of a rectangle is increased by 20%, then what will be the increment in area of rectangle?

a) 33.33%

b) 55%

c) 32%

d) 64%

e) 66.66% Radius of the cylinder = r = $\frac{14}{2}$ = 7

Height of the cylinder = h =14

Volume = Pi x r2 x h

= $\frac{22}{7}$ x 7 x 7 x 14 = 2156

Let the required number of rounds be x.

More radius, less rounds (Inverse Proportion)

15 == 125

25 == x

⟹ x=(15 * 125)/25 = 75 rounds

This is a right-angled triangle with the perpendicular sides being 5 and 6. So, area = ½ * 5 * 6 = 15 sq units

Let the width of the footpath be w.
So, area of the footpath = (30+2w)*(20+2w) – 20*30 = 216
From the options, w = 2 satisfies the equation. So, option a) is the answer.

One of the angles of a right-angled triangle should be 90 degrees. If the angles are in the ratio 5:6:7, the angles will be 50 degrees, 60 degrees and 70 degrees. So, 5:6:7 cannot be the ratio.

Triangle ADE is similar to triangle ABC. If the sides are in the ratio a:b, the areas will be in the ratio $a^2 : b^2$.
Here, the ratio of sides BC and DE is 2:1, so the ratio of areas of triangle ABC and triangle ADE will be 4:1.

If the sides of a right-angled triangle are in AP, then the sides are in the ratio 3:4:5. Since the largest side is 10 cm, the lengths of the other sides are 6 cm and 8 cm. So, the area of the triangle is ½ * 6 * 8 = 24 $cm^2$

Let the sides be 10l and 10b. So, area = 100lb.
Sides after the change = 12.5l and 7.5b
New area = 12.5l*7.5b = 93.75lb
So, percentage change in area = 6.25%

Let the sides be 10l and 10b.
Perimeter = 20l + 20b
New sides = 12.5l and 7.5b
New perimeter = 25l+15b
Change in perimeter = 5l – 5b
Percentage change in perimeter = (5l-5b)/(20l+20b)
So, the absolute change in percentage cannot be determined.

By Appolonius’ theorem, $AB^2$ + $BC^2$ = 2*($AD^2$ + $BD^2$)
100 + 81 = 2*($BD^2$ + 16) => BD = $\sqrt{90.5 – 16}$ = $\sqrt{74.5}$

Let the side be s cms long. Diagonal = $s \sqrt{2}$ and area = $s^{2}$
but area = 100. So, s = 10. So, diagonal = $10\sqrt {2}$

The area of a circle is pi*r*r. Area of the square = r*r. So, the area of the circle = pi*area of square = 3.14*100 = 314 sq.m

$S^{2} = pi * r^{2}$. So, s/r = $\sqrt \pi$

If two sides of the right angled triangle are equal, it is a right angled isosceles triangle. So, the angles of the triangle are 45, 45 and 90.

If the breadth is s, length is 2s and area = 2s * s = 50. So, s is 5 and 2s is 10.

If the perimeter of the rectangle is 84, 2 * (l + b) = 84. So, breadth is 18 metres since length is 24. $diagonal^{2} = length^{2} + breadth^{2}$. So, diagonal = 30. Area of the triangle = ½*base*height = ½* 18*30 = 270

Circumference = 2*$\pi$*r = 100 $\pi$. So, r = 50 metres. Area = $\pi$* r * r = 2500 $\pi$

The required ratio is 2*$\pi$*r : 4*r = $\pi$:2

This is a symmetric right angled traingle. So, the angles will be 45, 45 and 90.

If the breadth is x, length = 3x. Perimeter = 2*(x+3x) = 544. so, breadth = 68 and length = 204. Area = 68*204

length of diagonal = $\sqrt{100}$*$\sqrt{2}$ = diameter. Radius = diameter/2. Area = $\pi$*$radius^{2}$

The number of diagonals of an n-sided polygon is $^nC_2 – n$. So, $^nC_2 – n = n + 3$ => $n^2 – n = 4n + 6$. Solving this, we get n = 6.

Ratio of area will be equal to ratio of height i.e. equal to = 1.25h/h = 5/4

Area is directly proportional to the square of its radius; Let’s say radius is r and area is $\pi r^2$
Hence new radius is 5r/3 , and new area = $25\pi r^2/9$
Increment in area = $16\pi r^2/9$ 