Grade 9 : Mathematics - 8. Mensuration (Set 4)

Question 1

The sides of a triangular field are in the ratio $13 : 14 : 15$ and its perimeter is 84 cm. What is the area of the triangle?

Accepted Answer

B) $336cm^2$

Answer

A) $288cm^2$

Answer

C) $360cm^2$

Answer

D) $420cm^2$

Question 2

A circular running track is formed by two concentric circles. The inner circumference of the track is 220 m and the outer circumference is 264 m.

Calculate the width of the running track (Take $\pi = \frac{22}{7}$).

Accepted Answer

A) 7 m

Answer

B) 14 m

Answer

C) 10.5 m

Answer

D) 3.5 m

Question 3

A rectangular wooden box has dimensions $12cm imes 9cm imes 8cm$. What is the length of the longest rod that can be placed inside this box?

Accepted Answer

C) 17 cm

Answer

A) 15 cm

Answer

B) 16 cm

Answer

D) 19 cm

Question 4

A right circular cone has a vertical height of 12 cm and a slant height of 13 cm. What is the volume of the cone in terms of $\pi$?

Accepted Answer

A) $100\picm^3$

Answer

B) $300\picm^3$

Answer

C) $150\picm^3$

Answer

D) $60\picm^3$

Question 5

An open cylindrical water tank with radius 7 m and height 10 m needs to be painted on its outer curved surface and its outer base.

Find the total cost of painting the tank at the rate of ₹15 per $m^2$ (Take $\pi = \frac{22}{7}$).

Accepted Answer

D) ₹8,910

Answer

A) ₹6,600

Answer

B) ₹7,425

Answer

C) ₹8,150

Question 6

The total surface area of a solid hemisphere of radius 21 cm is (Take $\pi = \frac{22}{7}$):

Accepted Answer

B) $4158cm^2$

Answer

A) $2772cm^2$

Answer

C) $5544cm^2$

Answer

D) $1386cm^2$

Question 7

The area of a trapezium-shaped plot is $480m^2$. If the parallel sides measure 24 m and 16 m, find the distance between them.

Accepted Answer

C) 24 m

Answer

A) 12 m

Answer

B) 18 m

Answer

D) 30 m

Question 8

The lengths of the two diagonals of a rhombus are 16 cm and 12 cm. What is the perimeter of the rhombus?

Accepted Answer

A) 40 cm

Answer

B) 56 cm

Answer

C) 48 cm

Answer

D) 32 cm

Question 9

An isosceles triangle has two equal sides of length 10 cm each and a base of length 12 cm. Using Heron's formula, find its area.

Accepted Answer

D) $48cm^2$

Answer

A) $60cm^2$

Answer

B) $36cm^2$

Answer

C) $54cm^2$

Question 10

The total surface area of a cube is $384cm^2$. What is the volume of this cube?

Accepted Answer

B) $512cm^3$

Answer

A) $216cm^3$

Answer

C) $343cm^3$

Answer

D) $729cm^3$

Question 11

A solid iron sphere of radius 3 cm is melted and recast into small spherical marbles of radius 0.5 cm each. How many marbles can be made?

Accepted Answer

C) 216

Answer

A) 64

Answer

B) 108

Answer

D) 432

Question 12

A solid metallic cylinder of base radius 6 cm and height 12 cm is melted and recast into a cone of height 16 cm. Find the radius of the cone.

Accepted Answer

A) 9 cm

Answer

B) 8 cm

Answer

C) 12 cm

Answer

D) 6 cm

Question 13

Container	Radius ($r$)	Height ($h$)
Container A	7 cm	10 cm
Container B	14 cm	5 cm
Container C	7 cm	15 cm

Based on the table above showing dimensions of cylindrical containers, what is the difference in volume between Container B and Container A? (Take $\pi = \frac{22}{7}$)

Accepted Answer

B) $1540cm^3$

Answer

A) $770cm^3$

Answer

C) $2310cm^3$

Answer

D) $3080cm^3$

Question 14

A square park has side length 28 m. A circular flowerbed is constructed inside it such that it touches all four sides of the park.

Calculate the remaining area of the park outside the flowerbed (Take $\pi = \frac{22}{7}$).

Accepted Answer

C) $168m^2$

Answer

A) $112m^2$

Answer

B) $144m^2$

Answer

D) $224m^2$

Question 15

The curved surface area of a right circular cone is $550cm^2$. If its base radius is 7 cm, what is its slant height? (Take $\pi = \frac{22}{7}$)

Accepted Answer

D) 25 cm

Answer

A) 15 cm

Answer

B) 20 cm

Answer

C) 22 cm

Question 16

A wooden toy is made in the shape of a cylinder surmounted by a hemisphere. Both have a common radius of 3 cm. The height of the cylindrical part is 7 cm.

Find the total volume of the toy in terms of $\pi$.

Accepted Answer

B) $81\picm^3$

Answer

A) $63\picm^3$

Answer

C) $99\picm^3$

Answer

D) $108\picm^3$

Question 17

A quadrilateral plot has a diagonal of length 24 m. The perpendicular distances from the opposite two vertices to this diagonal are 8 m and 12 m. What is the total area of the plot?

Accepted Answer

A) $240m^2$

Answer

B) $288m^2$

Answer

C) $192m^2$

Answer

D) $480m^2$

Question 18

A cylindrical hollow iron pipe is 20 cm long. Its outer radius is 4 cm and inner radius is 3 cm. Find the volume of iron used in making the pipe (Take $\pi = \frac{22}{7}$).

Accepted Answer

C) $440cm^3$

Answer

A) $220cm^3$

Answer

B) $330cm^3$

Answer

D) $880cm^3$

Question 19

If the radius of a sphere is doubled, by what percentage does its surface area increase?

Accepted Answer

D) 300%

Answer

A) 100%

Answer

B) 200%

Answer

C) 250%

Question 20

A farmer owns a triangular field with side lengths 50 m, 78 m, and 112 m.

Calculate the total cost of leveling the field at the rate of ₹5 per $m^2$.

Accepted Answer

A) ₹8,400

Answer

B) ₹7,200

Answer

C) ₹9,600

Answer

D) ₹10,500

Grade 9 : Mathematics - 8. Mensuration (Set 4)