Grade 9 : Mathematics - 8. Mensuration (Set 3)

Question 1

A triangular park has sides measuring 13 m, 14 m, and 15 m.

Calculate the cost of turfing the park at ₹15 per $m^2$.

Accepted Answer

B) ₹1260

Answer

A) ₹1120

Answer

C) ₹1350

Answer

D) ₹1480

Question 2

If the radius of a right circular cylinder is doubled while keeping its height constant, by what factor does its volume increase?

Accepted Answer

C) 4 times

Answer

A) 2 times

Answer

B) 3 times

Answer

D) 8 times

Question 3

A conical tent has a vertical height of 12 m and a base radius of 5 m.

What is the curved surface area of canvas required to make the tent?

Accepted Answer

B) $65\pim^2$

Answer

A) $60\pim^2$

Answer

C) $78\pim^2$

Answer

D) $90\pim^2$

Question 4

A solid metallic sphere of radius 6 cm is melted and recast into a solid right circular cylinder of height 8 cm. What is the radius of the cylinder?

Accepted Answer

C) 6 cm

Answer

A) 4 cm

Answer

B) 5 cm

Answer

D) 8 cm

Question 5

Find the total surface area of a solid hemisphere of radius 7 cm. (Use $\pi = \frac{22}{7}$)

Accepted Answer

B) $462cm^2$

Answer

A) $308cm^2$

Answer

C) $616cm^2$

Answer

D) $154cm^2$

Question 6

A cube of edge $a$ and a sphere of radius $r$ have equal total surface areas. What is the ratio of the volume of the cube to the volume of the sphere?

Accepted Answer

A) $\sqrt{\pi} : \sqrt{6}$

Answer

B) $\sqrt{6} : \sqrt{\pi}$

Answer

C) $\pi : 6$

Answer

D) $6 : \pi$

Question 7

The sides of a triangular field are in the ratio $5 : 12 : 13$ and its perimeter is 300 m.

Find the area of the field.

Accepted Answer

C) $3000m^2$

Answer

A) $1500m^2$

Answer

B) $2500m^2$

Answer

D) $6000m^2$

Question 8

The areas of three adjacent faces of a rectangular cuboid are $12cm^2$, $15cm^2$, and $20cm^2$. What is the volume of the cuboid?

Accepted Answer

B) $60cm^3$

Answer

A) $45cm^3$

Answer

C) $90cm^3$

Answer

D) $120cm^3$

Question 9

A cylindrical pillar has a radius of 21 cm and a height of 4 m. Find the cost of painting its curved surface at ₹25 per $m^2$. (Use $\pi = \frac{22}{7}$)

Accepted Answer

B) ₹132

Answer

A) ₹110

Answer

C) ₹154

Answer

D) ₹176

Question 10

The area of a rhombus is $96cm^2$. If one diagonal is 16 cm, find the length of the other diagonal and the side length of the rhombus.

Accepted Answer

A) 12 cm and 10 cm

Answer

B) 10 cm and 8 cm

Answer

C) 14 cm and 10 cm

Answer

D) 12 cm and 8 cm

Question 11

The parallel sides of a trapezium are 25 cm and 15 cm, and the distance between them is 10 cm. What is the area of the trapezium?

Accepted Answer

C) $200cm^2$

Answer

A) $150cm^2$

Answer

B) $180cm^2$

Answer

D) $250cm^2$

Question 12

An isosceles triangle has two equal sides of length 10 cm each and a perimeter of 36 cm. Find its area using Heron's formula.

Accepted Answer

C) $48cm^2$

Answer

A) $36cm^2$

Answer

B) $42cm^2$

Answer

D) $54cm^2$

Question 13

If the radius of a cone is doubled and its height is halved, how does its volume change compared to the original volume?

Accepted Answer

B) Doubled

Answer

A) Remains unchanged

Answer

C) Quadrupled

Answer

D) Halved

Question 14

A hollow metallic pipe of length 20 cm has an outer radius of 5 cm and an inner radius of 4 cm. What is the volume of metal used to make the pipe?

Accepted Answer

C) $180\picm^3$

Answer

A) $140\picm^3$

Answer

B) $160\picm^3$

Answer

D) $200\picm^3$

Question 15

A solid sphere has a surface area numerically equal to its volume. What is the radius of the sphere?

Accepted Answer

C) 3 units

Answer

A) 1 unit

Answer

B) 2 units

Answer

D) 4 units

Question 16

Container	Type	Dimensions
A	Cuboid	$l = 10cm, w = 8cm, h = 15cm$
B	Right Cylinder	$r = 7cm, h = 10cm$

Which container has greater capacity and by how much? (Use $\pi = \frac{22}{7}$)

Accepted Answer

B) Container B by $340cm^3$

Answer

A) Container A by $340cm^3$

Answer

C) Container B by $240cm^3$

Answer

D) Container A by $140cm^3$

Question 17

Water flows at a rate of 0.5 m/s through a circular pipe of internal diameter 14 cm into a rectangular tank of length 11 m and width 7 m.

How much does the water level rise in the tank after 1 hour? (Use $\pi = \frac{22}{7}$)

Accepted Answer

C) 36 cm

Answer

A) 28 cm

Answer

B) 32 cm

Answer

D) 40 cm

Question 18

In a quadrilateral field ABCD, diagonal $AC = 24m$. Perpendiculars dropped from vertices $B$ and $D$ onto AC are 8 m and 12 m respectively. What is the area of the field?

Accepted Answer

C) $240m^2$

Answer

A) $200m^2$

Answer

B) $220m^2$

Answer

D) $280m^2$

Question 19

A cone, a hemisphere, and a cylinder stand on equal bases and have the same height (height equals base radius $r$). What is the ratio of their volumes?

Accepted Answer

A) $1 : 2 : 3$

Answer

B) $3 : 2 : 1$

Answer

C) $1 : 3 : 2$

Answer

D) $2 : 1 : 3$

Question 20

If each edge of a cube is increased by 50%, what is the percentage increase in its total surface area?

Accepted Answer

C) 125%

Answer

A) 50%

Answer

B) 100%

Answer

D) 150%

Grade 9 : Mathematics - 8. Mensuration (Set 3)