Q 1 – If the radius of a cylinder is 4cm and height is 10cm, then the total surface area of a cylinder is:
a. 440 sq.cm
b. 352 sq.cm
c. 400 sq.cm
d. 412 sq.cm
b. 352 sq.cm
Q 2 – If slant height of the cone is 21cm and the diameter of the base is 24 cm. The total surface area of a cone is:
a. 1200.77 sq.cm
b. 1177 sq.cm
c. 1222.77 sq.cm
d. 1244.57 sq.cm
d. 1244.57 sq.cm
Q 3 – The number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit that is 16 m long, 12m wide and 4 m deep is
(a) 1900
(b) 1920
(c) 1800
(d) 1840
(b) 1920
Q 4 – Match the column: [5]
Curved surface area of Cone | 3π r2 |
Curved surface of Hemisphere | 2π rh |
Curved surface area of Cylinder | 2π r2 |
Total surface area of Hemisphere | πr2 +πrl |
Total surface area of cone | πrl |
Curved surface area of Cone | πrl |
Curved surface of Hemisphere | 2π r2 |
Curved surface area of Cylinder | 2π rh |
Total surface area of Hemisphere | 3π r2 |
Total surface area of cone | πr2 +πrl |
Q 5 – Hameed has built a cubical water tank with a lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see Fig.). Find how much he would spend for the tiles if the cost of the tiles is Rs 360 per dozen.
Given,
Edge of the cubical tank (a) = 1.5 m = 150 cm
So, surface area of the tank = 5 × 150 × 150 cm2
The measure of side of a square tile = 25 cm
Area of each square tile = side × side = 25 × 25 cm2
Required number of tiles = (Surface area of the tank)/(area of each tile)
= (5 × 150 × 150)/(25 × 25)
= 180
Also, given that the cost of the tiles is Rs. 360 per dozen.
Thus, the cost of each tile = Rs. 360/12 = Rs. 30
Hence, the total cost of 180 tiles = 180 × Rs. 30 = Rs. 5400
Q 6 – The paint in a certain container is sufficient to paint an area equal to 9.375 sq.m. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
Given,
Dimensions of the brick = 22.5 cm × 10 cm × 7.5 cm
Here, l = 22.5 cm, b = 10 cm, h = 7.5 cm
Surface area of 1 brick = 2(lb + bh + hl)
= 2(22.5 × 10 + 10 × 7.5 + 7.5 × 22.5) cm2
= 2(225 + 75 + 168.75) cm2
= 2 x 468.75 cm2
= 937.5 cm2
Area that can be painted by the container = 9.375 m2 (given)
= 9.375 × 10000 cm2
= 93750 cm2
Thus, the required number of bricks = (Area that can be painted by the container)/(Surface area of 1 brick)
= 93750/937.5
= 937500/9375
= 100
Q 7 – A circus tent consists of cylindrical base surmounted by a conical roof. The radius of the cylinder is 20 m. The height of the tent is 63 m and that of the cone is 21 m. find the area of the canvas used for making it.
Radius of the base is r=20 m
Height of the tent h=63 m
Height of the conical part is H=21 m
Volume of the tent = Volume of cylinder + Volume of the cone
Now, the slant height is
Curved surface area of the tent = area of cylinder + Area of cone
Q 8 – A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide, and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
(i) Lateral surface area of cube = edge2
= 400
lateral surface area of cuboid = (l+b)
(12.5 + 10)
=16 × 22.5
= 360
So, the lateral surface area of the cube is larger by 2
(ii) Total surface area of cube = 2
= 600
lateral surface area of cuboid = (lb + bh + hl)
+ 10 × 8 + 8 × 12.5)
= 2 (125 + 80 + 100)
= 610
So, the total surface area of the cuboid is larger by – 600 = 10) 2
Q 9 – Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope.(see Fig).
What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius? You may take 
R
Radius of the base of the cylindrical kaleidoscope (r) = 3.5 cm.
Height (length) of kaleidoscope (h) = 25 cm.
Area of chart paper required = curved surface area of the kaleidoscope
Q 10 – A 20 m deep well with diameter 14 m is dug up and the earth from digging is evenly spread to form a platform 22 m 14 m. Find the height of the platform.
Q 11 – Find the total surface area of a cone, if its slant height is 21 m and the diameter of its base is 24 m.
Given,
Slant height of cone is l = 21 m.
Diameter of its base is d = 24 m.
hence, radius of its base is 
= 12m.
Now, the total surface area of cone is given by
S = πrl + πr2
S = π (rl + r2)
S = π (12 × 21 + 122)
S = π (252 + 144)
S = 
× 396
hence, S = 1244.57m2
Q 12 – The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
The inner diameter of the hollow sphere, 2r =7m
Available area to the motorcyclist for riding = Inner surface area of the sphere
=4πr2=π(2r)2
Available area to the motorcyclist for riding =154sq.m