Class 9 Maths Important Questions for Surface area and volume

Given below are the Class 9 Maths Important Questions for Surface area and volume
(a) Concepts questions
(b) Calculation problems
(c) Multiple choice questions
(e) Fill in the blank's

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
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
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
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
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
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
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
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
 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 $\pi r\sqrt{r^{2}+H^{2}}$