Given below are the Class 9 MathsExtra questions and Important Questions for Surface area and volume
(a) Concepts questions
(b) Calculation problems
(c) Multiple choice questions
(d) Long answer 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 cm^{2} / 700 cm^{2}/ 800 cm^{2}) (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 ___ (1800cm^{3}/1728 cm^{3}) (d) The total surface area of a hemisphere of radius 10 cm using value of π=3.14 is _____(956 cm^{2}/942 cm^{2}) (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 m^{2}, the volume is ____ (456 m^{3}/512 m^{3}) Solution
(a) Remain same
CSA= 2πrh
So if r is doubled, h is halved,CSA will remain same
(b) 616 cm^{2}, Surface area=4πr^{2}
(c) 1728 cm^{3}, V=V_{1} + V_{2} + V_{3}=6^{3}+ 8^{3} +10^{3}
(d) 956 cm^{2}, Total surface area =3πr^{2}
(e) 1:1 In this height of cylinder will be 2r and radius of cylinder will r. So it is equal
(f) 512 m^{3}, Lateral surface area=4a^{2} and Volume=a^{3}c
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. 48000m^{3} 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 =πr^{3}
Hemisphere=(2/3) πr^{3}
Cone=(1/3) πr^{3}
So ratio is 3:2:1
(b) True. Sphere volume =(4/3) πr^{3}
(c) False. Volume will be doubled. Volume is given by =(1/3)πr^{2}h
(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 m^{2}
(b) 516 m^{2}
(c) 800 m^{2}
(d) 456m^{2} Solution
Answer is (b)
Area of the walls is given by =2(BH+LH) +LB=2(90+108)+120=516 m^{2}
Question 4
The plastic paint in a Asian paint container is sufficient to paint an area equal to 93.75m^{2} 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) cm^{2}
= (2 × 468.75) cm^{2}
= 937.5 cm^{2}
Let n blocks can be painted out by the paint of the container.
Area of n bricks = (n ×937.5) cm^{2} = 937.5n cm^{2}
Area that can be painted by the paint of the container = 93.75 m^{2}= 937500 cm^{2}
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 cm^{2} and its slant height is 14 cm.
(a) Radius of the cone is 7 cm
(b) total surface area is 462 cm^{2}
(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=πr^{2}+πrl=462 cm^{2}
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 cm^{2}
(b) 1400 cm^{2}
(c) 986 cm^{2}
(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)πr^{2}h
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 cm^{2}. Find the Volume of the cylinder. Assume π=22/7
(a) 144 cm^{3}
(b) 180 cm^{3}
(c) 176 cm^{3}
(d) None of the above Solution
Answer is (c)
Match the column
Question 11
Subjective Type questions
Question 12
Ramesh has build a cuboidal water tank with lid for his house with each outer edge 1.5m long. He gets the outer surface of tank excluding the base, covered with square tiles of side 25cm. Find how much he would spend for tiles, if cost of the tile is Rs 400 per dozen. Solution
Surface Area of the cuboidal water tank where tiles to be placed= 5L^{2}= 11.25 m^{2}
Area of 1 Tile= 25^{2}=625 cm^{2}=.0625 m^{2}
No of Tiles required=11.25/.0625=180=15 dozen
Cost of tiles will be = 400 * 15=Rs 6000
Question 13
The paint in a certain container is sufficient to point an area equal to 9.375m^{2}. How many bricks of dimensions 22.5cm x 10cm x 7.5cm can be painted out of this container. Solution
Surface are of 1 Brick= 2(LB+ BH+ LH)=2(225 + 75 + 168.75)=937.5 cm^{2}
Total Brick which can be painted= $\frac {9.375 \times 10^4}{937.5}= 100
Question 14
Bikanerwala sweets shop was planning an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25cm x 20cm x 5cm and smaller of dimensions 15cm x 12cm x 5cm. For all overlaps, 5% of total surface area is required extra. If cost of cardboard is Rs 4 for 1000cm^{2}, find the cost of cardboard required for supplying 250 boxes of each kind.
Question 15
The diameter of a roller are 84cm and its length is 120cm. It takes 500 complete revolutions to move once more over to level a playground. Find area of playground in m^{2}? Solution
Diameter =84 cm, Therefore radius=42 cm
Curved Surface area of cylinder= $2 \pi r h= 2 \times \frac {22}{7} \times 42 \times 120 $ =31680 cm^{2}= 3.1680 m^{2}
Area of playground=500 × 3.1680=1584 m^{2}
Question 16
In a hot water heating system, there is a cylindrical pipe of length 28m and diameter 5cm. Find the total radiating surface in system? Solution
Diameter =5 cm, Therefore radius=2.5 cm
Curved Surface area of cylinder is the radiating surface= $2 \pi r h= 2 \times \frac {22}{7} \times 2.5 \times 2800 =44000$ cm^{2}
Question 17
Find
(a)the lateral or C.S.A of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5m in high
(b)how much steel was actually used, if 1/12 of steel actually used was wasted in making the tank. Question 18
You see the frame of lamp shade. It is to be covered with decorative cloth. The frame has a base diameter of 20cm and height of 30cm. A margin of 2.5cm is total given for folding it over top and bottom of frame How much cloth is required for covering the lamp shade? Question 19
What length of tarpaulin 3m wide will be required to make a conical tank of height 8m and base radius 6m. Assume that the extra length margins and wastage n cutting is approximately 20cm. (Use = 3.14) Question 20
A Birthday cap is in form of right circular cone of radius 7cm and height 24cm. Find area of sheet required to make 10 such caps? Question 21
A bus stop is barricaded from remaining part of road, by using 50 hollow cones made of recycles cardboard. Each cone has a base diameter of 4cm and height 1m. If outer side of earn cone is to be painted and cost of painting is Rs 12/m^{2}. What will be the cost? ( = 3.14 and take 1.04 = 1.02) Question 22
A hemispherical dome of a building needs to be painted. If circumference of base of dome is 17.6m, find the cost of painting it, given cost of painting is Rs. 5/200 cm^{2}. Question 23
The diameter of moon is approximately one – fourth diameter of earth. Find the ratio of their surface areas. and What fraction of the volume of the earth is the volume of the moon? Solution
Let d be diameter of earth
Surface area of earth= $ \pi d^2$
Diameter of Moon=$\frac {1}{4}d$
Surface area of Moon= $\pi D^2= \frac {1}{16} \pi d^2$
$\frac {\text{surface area of Moon}}{\text{surface area of earth}}= \frac {1}{16}$
Volume of earth=$\frac {1}{6} \pi d^3$
Surface area of Moon= $\frac {1}{6} \pi D^3= \frac {1}{384} \pi d^2$
$\frac {\text{Volume of Moon}}{\text{Volume of earth}}= \frac {1}{384}$
Question 24
A right circular cone just enclosed a sphere of radius r. Find –
(a)surface area of sphere
(b)curved surface area of cylinder
(c)ratio of areas obtained in (i) and (ii) Solution
(i) Surface area of a sphere where r is the radius of the sphere =$4 \pi r^2$
(ii) Height of the cylinder, =diameter of the sphere=2r
And Radius of the cylinder =r
CSA of cylinder formula = $2 \pi r h=4 \pi r^2$
(iii) Ratio between areas = $\frac {4 \pi r^2}{4 \pi r^2}=1:1$
Question 25
A wall of length 10m was to be built across an open ground. The height is 4m and thickness is 24cm. If this wall is to be build up with bricks whose dimensions are 24cm x 12cm x 8cm, how many bricks would be required? Question 26
Three cubes of each side 4cm are joining end to end. Find the surface area of resulting cuboid Solution
Surface of the cuboid will be =$ 4 \times 4 \times 12 + 2 \times 4 \times 4=224$ cm^{2}
Question 27
A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20m x 15m x 6m for how many days will the water of this tank last? Question 28
A godown measures 40m x 25m x 10m. Find the maximum no. of wooden crates each measuring 1.5m x 1.25m x 0.5m that can be stored in godown? Question 29
A river 3m deep and 40m wide is flowing at the rate of 2km/hr. How much water will fall into the sea in a minute? Solution
Speed of water in a river=2 km/hr
Length of flow of water in 1 minute= $\frac {2}{60} km =\frac {100}{3}m $
Therefore Volume of water
$=LBH= \frac {100}{3} \times 3 \times 40=4000 m^3 $
Volume in litres= 4000 * 1000= 4 × 10^{6}
Question 30
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20cm and height 10m. How much concrete mixture would be required to build 14 such pillars? Solution
Volume of single pillar= $\pi r^2 h=.2 \pi$
Volume of 14 Pillars= $ 14 \times .2 \pi=8.8 m^3$
Summary
This Surface area and volume class 9 extra questions with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.