Class 9 Maths Important Questions for Surface area and volume

Fill in the blank

Question 1
(a) A cylinder radius is doubled and height is halved, the curved surface area of the cylinder will ____ (Increase/decrease/remain same)
(b) The radius of the sphere is 7 cm, the surface area of the sphere is____ (616 cm² / 700 cm²/ 800 cm²)
(c) Three cubes whose sides are 6 cm, 8 cm and 10 cm. They are melted and form a big cube. The volume of the big cube is ___ (1800cm³/1728 cm³)
(d) The total surface area of a hemisphere of radius 10 cm using value of π=3.14 is _____(956 cm²/942 cm²)
(e) A right circular cylinder just encloses a sphere of radius. The ratio of there surface area is ______ (1:1 / 1:2)
(f) The lateral surface area of a cube is 256 m², the volume is ____ (456 m³/512 m³)
Solution
(a) Remain same
CSA= 2πrh
So if r is doubled, h is halved,CSA will remain same
(b) 616 cm²,  Surface area=4πr²
(c) 1728 cm³, V=V₁ + V₂ + V₃=6³+ 8³ +10³
(d) 956 cm², Total surface area =3πr²
(e) 1:1 In this height of cylinder will be 2r and radius of cylinder will r. So it is equal
(f) 512 m³, Lateral surface area=4a² and Volume=a³c

True or False statement

Question 2
(a) A cylinder, hemisphere and cone stand on equal base and same height, the Volume ratio is 3:2:1
(b) The radius of a solid sphere is 24 cm. 8 spheres can be made from it of 12cm radius
(c) radius of the cone is doubled and height is halved, the volume will be halved
(d) A river 10m deep and 40m wide is flowing at the rate of 2m per min. 48000m³ water will flow into the sea from river
(e) A cylinder radius is halved and height is doubled, the volume will become halved
(f) The side of the cube is 4 cm, the diagonal length is  cm
Solution
(a)True.. All of them will have height as r as hemisphere height can be r only. For cylinder  =πr³
Hemisphere=(2/3) πr³
Cone=(1/3) πr³
So ratio is 3:2:1

(b) True. Sphere volume =(4/3) πr³

(c) False. Volume will be doubled. Volume is given by =(1/3)πr²h

(d) True. It is equal to the volume of the cuboid  10m,40m,and 120 m

(e) True.

(f)False

Multiple choice Questions

Question 3
The length, breadth and height of a room are 12 m, 10 m, and 9m respectively. Find the area of  our walls of room?
(a) 636 m²
(b) 516 m²
(c) 800 m²
(d) 456m²
Solution
Answer is (b)
Area of the walls is given by =2(BH+LH) +LB=2(90+108)+120=516 m²

Question 4
The plastic paint in a Asian paint container is sufficient to paint an area equal to 93.75m² How many blocks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container
(a) 100
(b) 800
(c) 940
(d) 1000
Solution
Answer is (d)
Total surface area of one block = 2(lb + bh + lh)
= [2(22.5 ×10 + 10 × 7.5 + 22.5 × 7.5)] cm
= 2(225 + 75 + 168.75) cm²
= (2 × 468.75) cm²
= 937.5 cm²
Let n blocks can be painted out by the paint of the container.
Area of n bricks = (n ×937.5) cm² = 937.5n cm²
Area that can be painted by the paint of the container = 93.75 m²= 937500 cm²
937500 = 937.5n
n = 1000
Therefore, 1000 blocks can be painted out by the paint of the container

Question 5
Curved surface area of a cone is 308 cm² and its slant height is 14 cm.
(a) Radius of the cone is 7 cm
(b) total surface area is 462 cm²
(c) Height of the cone is $\sqrt {147}$ cm
(d) None of the above
Solution
Answer is (a),(b),(c)
Curved surface area=πrl
So r=7 cm
Now total surface area=πr²+πrl=462 cm²

Question 6
Sita had to make a model of cylindrical kaleidoscope for her science project. She wanted to use black chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 30cm with a 2.7 cm radius? (Use p=22/7)
(a)1320 cm²
(b) 1400 cm²
(c) 986 cm²
(d) None of these
Solution
Answer is a
Curved surface of cylinder=2πrh

Question 7
The radii of two cones are in the ratio of 2:3 and their heights are in the ratio of 7:3. The ratio of their volumes is
(a) 20:27
(b) 28:27
(c) 28:27
(d) None of these
Solution
Answer is (c)
Volume =(1/3)πr²h

Question 8
Find the maximum length of the rod that can be kept in cuboidal box of sides 30cm, 20cm and 10cm.
(a)$ \sqrt {1400}$ cm
(b)$2 \sqrt {400}$ cm
(c)$2 \sqrt {300}$ cm
(d) None of these
Solution
Answer is (a)
Diagonal is the longest length in the cuboid so
$D=\sqrt {L^2+B^2+H^2}$
=$ \sqrt {1400}$ cm

Question 9
A box is made entirely of glass panes (including base) held together with tape. It is 3 cm long, 2.5 cm wide and 2.5 cm high. How much of tape is needed for all the 12 edges?
(a) 30cm
(b) 32cm
(c) 40 cm
(d) None of these
Solution
Answer is (b)
Length of tape=4( L+B+H)=32 cm

Question 10
The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the Volume of the cylinder. Assume π=22/7
(a) 144 cm³
(b) 180 cm³
(c) 176 cm³
(d) None of the above
Solution
Answer is (c)

Match the column

Curved surface area of Cone	3πr2
Curved surface of Hemisphere	2πrH
Curved surface area of Cylinder	2πr2
Total surface area of Hemisphere	$\pi r^{2}+\pi r\sqrt{r^{2}+H^{2}}$
Total surface area of cone	$\pi r\sqrt{r^{2}+H^{2}}$

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• Notes
  • Surface Area and Volume Class 9 Notes
  • Surface area And volume Class 9 Formula Cheatsheet
• Assignments & NCERT
  • Surface Area and Volume Class 9 Practice Questions
  • Surface Area and Volume Class 9 Assignments
  • Surface Area and Volume Class 9 Worksheet
  • Surface Area and Volume Class 9 NCERT Solution Ex 13.1
  • Surface Area and Volume Class 9 NCERT Solution Ex 13.2
  • Surface Area and Volume Class 9 NCERT Solution Ex 13.3

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