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Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Class 9 MCQ


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25 Questions MCQ Test - Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics for Class 9 2024 is part of Class 9 preparation. The Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics questions and answers have been prepared according to the Class 9 exam syllabus.The Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics below.
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Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 1

Ratio of lateral surface areas of two cylinders with equal heights is :

Detailed Solution for Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 1
Formula of lateral surface area of cylinder is 2πrh as we know that their heights are equal and 2π is common in them the ratio of their radius will be R:r.
Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 2

Ratio of volumes of two cylinders with equal radii are :

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Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 3

The lateral surface area of cylinder is 176 cm2 and base area 38.5 cm2. The its volume is ____.

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 4

A cylinderical vessel contains 49.896 litres of liquid. cost of painting its CSA at 2 paise/sq cm is Rs. 95.04.

Then its total surface area is ______.

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 5

The area of the base of a cone is 616 sq cm. Its height is 48 cm. Then its total surface area is ____.

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 6

A vessel is in conical shape. If its volume is 33.264 litres and height is 72 cm, the cost of repairing its CSA

at Rs. 12/sq m is :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 7

From a circle of radius 15 cm a sector with 216° angle is cut out and its bounding radii are bent so as to

form a cone. Then its volume is :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 8

A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. The volume

of steel used is _____.

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 9

A cuboidal metal of dimensions 44 cm × 30 cm × 15 cm was melted and case into a cylinder of height 28

cm. Its radius is _____.

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 10

A piece of metal pipe is 77 cm long with inside diameter of the cross section as 4 cm. If teh outer diameter is

4.5 cm and the metal weighs 8 gm/cu cm, the weight of pipe is _____.

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 11

A circus tent is in the form of a cone over a cylinder. The diameter of the base is 9 m, the height of cylindrical

part is 4.8 m and the total height of the tent is 10.8 m. The canvas required for the tent is _____.

Detailed Solution for Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 11
Canvas required = CSA of cone + CSA of cylinder
csa of cone is 22/7 x r x l 
csa of cyl. is 2 x 22/7 x r x h     h of cone = 10.8 - 4.8
l=√(4.5)^2+(6 )^2= 7.5
canvas used= 22/7 x 4.5 x7.5 + 2 x22/7 x 4.5 x 4.8
                    =742.5/7 + 950.4/7
                    =106.07 + 135.77
                     = 241.84 cm^2

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 12

The diameter of a copper sphere is 6 cm. It is beaten and drawn into a wire of diameter 0.2 cm. The length

of wire is _____.

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 13

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base

diameter 8 cm. Find the height of the cone.

Detailed Solution for Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 13
External diameter of sphere = 8 cm 
rightwards double arrowradius, R = 4 cm
Internal diameter of sphere = 4 cm 
rightwards double arrowradius, r = 2 cm
Diameter of the base of cone = 8 cm 
rightwards double arrowradius = 4 cm
Now, Volume of the cone = Volume of the material in the sphere

Hence, the height of the cone = 14 cm      
Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 14

The radius of the cylinder whose lateral surface area is 704 cm2 and height 8 cm is :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 15

The ratio of the volume and surface area of a sphere of unit radius :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 16

Two identical right circular cones each of height 2 cm are placed as showin in diagram (each is vertical, apex downward). At the start, the upper cone is full of water and lower cone is empty.

Then water drips down through a hole in the apex of upper cone into the lower cone. The height of water in the lower cone at the moment when height of water in uper cone is 1 cm is :

 

Detailed Solution for Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 16
Assume the cone has a radius r and height h. Now initially the amount of water is pi r^2 h . Now since the new height is half of the initial height, the radius of the h/2  height cone is also half, using similarity. So final volume of water in top cone is .
pi ×(r/2)^2 ×(h/2).

So amount of water that drips down to bottom cone is .
pi ×r^2 ×h - pi × (r/2)^2 ×(h/2).= 7/8×pi ×r^2


Now let the height of water in the bottom cone be x, then using similarity, its radius is .
r × x/h

So the amount of water in the bottom cone is .
pi ×(r × x/h)^2. × X= 7/8×pi ×r^2 ×h..

pi n pi cancel out
putting h = 2 solve it then 8 is cancel out..
x^3= 7.
so answer= 3√7



So putting , we get . So the answer (d)
Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 17

A sphere and a cube are of the same height. The ratio of their volume is :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 18

The largest sphere is cut off from a cube of side 5 cm. The volume of the sphere will be :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 19

The edge of a cube is 20 cm. How many small cubes of 5 cm edge can be formed from this cube?

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 20

In the figure below, RSTV is a square inscribed in a circle with centre O and radius r. The total area of shaded region is :

 

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 21

Correct the perimeter of the figure given below to one decimal place :

 

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 22

A hollow spherical ball whose inner radius is 4 cm is full of water. Half of the water is transferred to a conical

cup and it completely filled' he cup. If the height of the cup is 2 cm, then the radius of the base of cone, in cm is :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 23

The largest volume of a cube that can be enclosed in a sphere of diameter 2 cm is (in cm3).

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 24

Each side of a cube is increased by 50%. Then the surface area of the cube increases by :

Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 25

The number of surfaces in right circular cylinder is :

Detailed Solution for Surface Area & Volumes - Olympiad Level MCQ, Class 9 Mathematics - Question 25
Definition:
 
A right circular cylinder is a three-dimensional object with two congruent circles as parallel bases and a lateral surface consisting of a rectangle.
Base and side: The bases of right circular cylinder are always congruent and parallel to each other. If you were to 'unroll' the cylinder you would find the side is actually a rectangle when flattened out.
Height: The height h is the perpendicular distance between the bases.
Radius: The radius r of a cylinder is the radius of a base.
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