Surface Areas And Volumes(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

SURFACE AREAS AND VOLUMES MCQs

Total Questions : 58 | Page 2 of 6 pages

Question 11. A juice seller fills juice into cylindrical glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹10/- for a glass of height 10 cm and radius 4 cm. The amount he earns by selling the juice is ____.

(U s e π = \frac{22}{7})

₹ 220/-
₹ 110/-
₹ 170/-
₹ 190/-

Discuss Question

Answer: Option A. -> ₹ 220/-
:
A
We know that,
volume of a cylinder

= π r^{2} h

Number of glasses of juice that are sold

= \frac{volumeof thevessel}{volumeofeachglass} = \frac{π \times 10 \times 10 \times 35.2}{π \times 4 \times 4 \times 10} = 22

∴

The amount earned by the shopkeeper

= Rate of each glass \times Total numberof glasses

= 10 \times 22 = ₹ 220 / -

Question 12. A water container can hold 40 litres of water. Then the total number of ice cubes of side 5 cm which the container can hold is ____.

Discuss Question

Answer: Option C. -> 320
:
C

1 litre = 1000 {cm}^{3}

40 litres = 40000 {cm}^{3}

Volume of water in the container

= 40 litres = 40000 {cm}^{3}

Volume of each ice cube

= (Side)^{3}

= 5^{3}

= 125 {cm}^{3}

∴

Number of ice cubes that can be fitted

= \frac{Volume of water container}{Volume of each cube}

= \frac{40000 {cm}^{3}}{125 {cm}^{3}}

= 320 ice cubes

Question 13. A

3 \times 3

Rubik's cube has a total surface area of

54 {cm}^{2}

. The area occupied by every single red tile of the cube is ___________ .

0.25 cm2
1 cm2
3 cm2
9 cm2

Discuss Question

Answer: Option B. -> 1 cm2
:
B
Given,
Total surface areaof the cube

= 54 {cm}^{2}

We know that,
Cube has 6 number of faces.
Eachface of the Rubik's cube contains 9 tiles.
EachRubik's cube contains 9 red tiles.

∴ Area of each face

= \frac{Totalsurfacearea of the cube}{Total numberof faces of the cube} = \frac{54}{6} = 9 {cm}^{2}

Now,

area of each tile

= \frac{Areaof eachface}{Totalnumber of tilesineachface} = \frac{9}{9} = 1 {cm}^{2}

Hence, the area occupied by every single red tile of the cube is

1 {cm}^{2}

Question 14. Pavan drew a

△

ABC right angled at B. He says if the right angle triangle is rotated along AB then it will result in ___

Cone
Cube
Cylinder
Cuboid

Discuss Question

Answer: Option A. -> Cone
:
A
If right angle triangle is rotated along any of it's perpendicular side then we will get a right circular cone. See the image below

Pavan Drew A △ABC Right Angled At B. He Says If The Right ...

Question 15. A big iron boiler tank which is cylindrical in shape is open at the top. Its height is 10

m

and radius is 7

m

. It gets corroded at a rate of 3

m^{2}

/day. The number of days it will take to corrode completely is ____ .

(u s e π = \frac{22}{7})

Discuss Question

Answer: Option C. -> 198
:
C
Surface area of the boiler = Curved surface area of boiler + Base area of boiler

= 2 π r h + π r^{2}

= 2 \times \frac{22}{7} \times 7 \times 10 + \frac{22}{7} \times 7^{2}

= 440 + 154

= 594 m^{2}

Now, number of days to corrode

= \frac{T o t a l S u r f a c e A r e a o f t a n k}{A r e a c o r r o d e d p e r d a y}

= \frac{594}{3}

= 198 d a y s

∴

Boiler will take 198 days to get corroded completely.

Question 16. The volume of a cone of radius 7

c m

and slant height 14

c m

is ______.

(u s e π = \frac{22}{7})

622.381 cm3
722.381 cm3
618.381 cm3
522.381 cm3

Discuss Question

Answer: Option A. -> 622.381 cm3
:
A
Given,
Radius of the cone

r = 7 c m

Slant height of the cone

l = 14 c m

The Volume Of A Cone Of Radius 7 Cm And Slant Height 14 Cm I...

From the pythagoras theorem

l^{2} = h^{2}

r^{2}

,
height of the cone

h = \sqrt{14^{2} - 7^{2}}

h = \sqrt{147} = 12.1243 c m

Volume of a Cone

= \frac{1}{3} \times π \times r^{2} h

= \frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 12.1243

= 622.381 c m^{3}

Question 17. A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. The volume of the solid formed is______.

144 cm3
132 cm3
154 cm3
169 cm3

Discuss Question

Answer: Option C. -> 154 cm3
:
C
We know that,
volume of cone

= \frac{1}{3} π r^{2} h

volumeof hemisphere

= \frac{2}{3} π r^{3}

Total volume
= Volume of the cone + Volume of the hemisphere

= \frac{1}{3} π r^{2} h + \frac{2}{3} π r^{3} = \frac{1}{3} π r^{2} (h + 2 r) = \frac{1}{3} \times \frac{22}{7} \times {3.5}^{2} \times (5 + 7) = \frac{1}{3} \times \frac{22}{7} \times {3.5}^{2} \times 12 = 22 \times 0.5 \times 3.5 \times 4 = 154 {cm}^{3}

∴

The volume of the solid formed is

154 {cm}^{3}

Question 18. Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____.

(U s e π = \frac{22}{7})

400 cm2
267 cm2
258 cm2
374 cm2

Discuss Question

Answer: Option D. -> 374 cm2
:
D
Given,
Radius

(r)

= 7

cm

Slant height

(l)

= 10

cm

Area of the aluminium sheet required
=Total surfacearea ofthe cone
=

π r (l + r)

\frac{22}{7} \times 7 (10 + 7)

= 374

{cm}^{2}

Hence, the area of the aluminium sheet required is 374

{cm}^{2} .

Question 19. In a circus, a motorcyclist performs his stunts inside a hollow sphere. The thickness of the sphere is negligible. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform his stunts.

(u s e π = \frac{22}{7})

516 m2
616 m2
586 m2
486 m2

Discuss Question

Answer: Option B. -> 616 m2
:
B
Radius of the sphere

= \frac{d i a m e t e r}{2} = \frac{14}{2} = 7 m

Area available to the motorcyclist = Surface area of the sphere

= 4 π r^{2}

= 4 \times \frac{22}{7} \times 7^{2}

= 616 m^{2}

Hence, the available area to the motorcyclist is 616

m^{2}

Question 20. Raghu needs to make a cylindrical aluminum tube. What will be the area of the aluminum sheet required to make the tube, if the length and radius of the tube should be 1