Chapter 16 Surface Areas and Volumes RD Sharma Solutions Exercise 16.2 Class 10 Maths
Chapter Name  RD Sharma Chapter 16 Surface Area and Volumes Exercise 16.1 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 16.2 Solutions
1. A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of
cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone
is 16 m above the ground. Find the area of canvas required for the tent.
Solution
Given diameter of cylinder 24m
2. A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached tot the top. The cylinder is of radius 2.5m and height 21m and the cone has a a slant height 8m. Calculate total surface area and volume of the rocket ?
Solution
Given radius of cylinder (a) = 2.5 m
Height of cylinder (h) = 21m
Slant height of cylinder (l) = 8m
3. A tent of height 77 dm is in the form of a right circular cylinder of diameter 36m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 350/m^{2} . (Use it 22/7)
Solution
4. A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy ?
Solution
Given height of cone(h) = 4cm
Diameter of cone (d) = 6cm
∴ Radius (r) = 6/2 = 3 cm
Solution
6 A cylindrical tube of radius 5cm and length 9.8cm is full of water. A solid in form of a right circular cone mounted on a hemisphere is immersed in tube. If radius of hemisphere is immersed in tube if the radius of hemisphere is 3.5cm and height of the cone outside hemisphere is 5cm. Find volume of water left in the tube?
Solution
Given radius of cylindrical tube (r) = 5cm.
Height of cylindrical tube (h) = 9.8cm
Volume of cylinder = Ï€r^{2} h
7. A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5cm and 13cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.
Solution
8. A circular tent has cylindrical shape surmounted by a conical roof. The radius of cylindrical base is 20 m. The height of cylindrical and conical portions are 4.2m and 2.1m. Find the volume of the tent ?
Solution
Given radius of cylindrical base = 20m
Height of cylindrical part (h) = 4.2m
Height of cylindrical part (h) = 4.2m
9. A petrol tank is a cylinder of base diameter 21cm and length 18cm fitted with conical ends each of axis 9cm. Determine capacity of the tank ?
Solution
Given base diameter of cylinder = 21cm
Radius (r) = 21/2 = 11.5cm
Height of cylindrical part (h) = 18cm
10. A conical hole is drilled in a circular cylinder of height 12cm and base radius 5cm. The height and base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder ?
Solution
11. A tent is in form of a cylinder of diameter 20m and height 2.5m surmounted by a cone of equal base and height 7.5m. Find capacity of tent and cost of canvas at Rs 100 per square meter ?
Solution
12. A boiler is in the form of a cylinder 2m long with hemispherical ends of 2m diameter. Find the volume of the boiler ?
Solution
13. A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of cylinder is 14/3 m and internal surface area of the solid ?
Solution
Given radius of hemisphere (r) = 3.5/2 = 1.75 m
Height of cylinder (h) = 14/3 m
Height of cylinder (h) = 14/3 m
14. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104cm and radius of each of hemispherical ends is 7cm. Find the cost of polishing its surface at the rate of Rs 10 per dm^{2}?
Solution
Given radius of hemispherical ends = 7cm
Height of body (h + 2r) = 104cm.
Height of body (h + 2r) = 104cm.
Curved surface area of cylinder = 2Ï€rh
= 2Ï€(7)h ...(1)
⇒ 4 + 2x = 104
⇒ h = 104  2(r)
⇒ h = 90cm
= 2Ï€(7)h ...(1)
⇒ 4 + 2x = 104
⇒ h = 104  2(r)
⇒ h = 90cm
Substitute 'h' value in (1)
Curved surface area of cylinder = 2Ï€(7)(90) = 3960 cm^{2} ...(2)
Curved surface area of 2 hemisphere = 2(2Ï€r^{2})
= 2(2×Ï€×7^{2}) = 616 cm^{3} ...(3)
Total curved surface area (2) + (3)
= 3960 + 616 = 4576 cm^{2} = 45.76dm^{2}
Cost of polishing for 1dm^{2} = Rs 10
Cost of polishing for 45.76 dm^{2} = 45.76 ×10 = Rs 457.6
Curved surface area of cylinder = 2Ï€(7)(90) = 3960 cm^{2} ...(2)
Curved surface area of 2 hemisphere = 2(2Ï€r^{2})
= 2(2×Ï€×7^{2}) = 616 cm^{3} ...(3)
Total curved surface area (2) + (3)
= 3960 + 616 = 4576 cm^{2} = 45.76dm^{2}
Cost of polishing for 1dm^{2} = Rs 10
Cost of polishing for 45.76 dm^{2} = 45.76 ×10 = Rs 457.6
15. A cylindrical vessel of diameter 14cm and height 42cm is fixed symmetrically inside a similar vessel of diameter 16cm and height 42cm. The total space between two vessels is filled with cork dust for heat insulation purpose. How many cubic cms of cork dust will be required ?
Solution
Given height of cylindrical vessel (h) = 42cm
16. A cylindrical road solar made of iron is 1m long its internal diameter is 54cm and thickness of the iron sheet used in making roller is 9cm. Find the mass of roller if 1cm^{3} of iron has 7.8 gm mas ?
Solution
17. A vessel in from of a hollow hemisphere mounted by a hollow cylinder. The diameter of hemisphere is 14cm and total height of vessel is 13cm. Find the inner surface area of vessel ?
Solution
Given radius of hemisphere and cylinder (r) = 14/2 = 7cm
Given total height of vessel = 13cm
(h + r) = 13cm
Inner surface area of vessel = 2Ï€r(h + r)
= 2 × Ï€ × 7 (13)
= 182 Ï€
= 572 cm^{2}
= 2 × Ï€ × 7 (13)
= 182 Ï€
= 572 cm^{2}
18. A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius. The total height of toy is 15.5cm. Find the total surface area of toy ?
Solution
19. The difference between outside and inside surface areas of cylindrical metallic pipe 14cm long is 44m^{2}. If pipe is made of 99 cm^{3} of metal. Find outer and inner radii of pipe?
Solution
We have to find the outer and inner radius of a hollow pipe.
Radius of inner pipe be(r_{1})
Radius of outer cylinder be (r_{2})
Length of the cylinder(h) = 14 cm
Difference between the outer and the inner surface area is 44 cm^{2}
So,
2Ï€h(r_{2}  r_{1}) = 44
inner pipe radius (r_{1}): 2 cm
outer cylinder (r_{2}): 2.5 cm
20. A radius circular cylinder bring having diameter 12cm and height 15 cm is full icecream. The icecream is to be filled in cones of height 12 cm and diameter 6cm having a hemisphere shape on top find the number of such cones which can be filled with icecream?
Solution
We have,
Radius of the cylincler = 12/2 = 6cm
Height of the cylinder = 15cm
∴ volume of the cylinder = Ï€r^{2}h
= Ï€× 6^{2} ×15
= 540Ï€cm^{3}
Radius of the icecream cone = 3cm
Height of the icecream cone = 12cm
∴ volume of the conical part of icecream
21. A solid iron pole having cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole given that the mass of 1 cm^{3} of iron is 8gm ?
Solution
Given radius of cylindrical part (r) = 12/2 = 6 cm
Height of cylinder (h) = 110 cm
Length of cone (l) = 9cm
Volume of cylinder = Ï€r^{2} h
22. A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2cm and the diameter of the base is 4cm. If a right circular cylinder circumscribes the toy find how much more space it will cover.
Solution
Given radius of cone, cylinder and hemisphere (r) = 4/2 = 2cm
Height of cone (l) = 2cm
Height of cylinder (h) = 4cm
Volume of cylinder = Ï€r^{2} h = Ï€(2)^{2} (4) cm^{3} ...(1)
Solution
Given radius of circular cone (a) = 60cm
Height of circular cone (b) = 120 cm.
24. A cylindrical vessel with internal diameter 10cm and height 10.5cm is full of water. A solid cone of base diameter 7cm and height 6cm is completely immersed in water. Find value of water (i) displaced out of the cylinder
(ii) left in the cylinder ?
Solution
25. A cylindrical vessel with internal diameter 10 cm and height 10.5cm is full of water. A solid cone of base diameter 7cm and height 6cm is completely immersed in water. Find value of water (i) displaced out of the cylinder (ii) left in the cylinder?
Solution
26. A hemispherical depression is cut from one face of a cubical wooden block of edge 21cm such that the diameter of hemisphere is equal to the edge of cube determine the volume and total surface area of the remaining block ?
Solution
Given edge of wooden block (a) = 21cm
Given diameter of hemisphere = edge of cube
Radius = 21/2 = 10.5cm
Volume of remaining block = volume of box  volume of hemisphere
27. A tag is in the form of a hemisphere surmounted by a right circular cone of same base radius as that of the hemisphere. If the radius of the base of cone is 21 cm and its volume is 2/3 of volume of hemisphere calculate height of cone and surface area of toy ?
Solution
28. A solid is in the shape of a cone surmounted on hemisphere the radius of each of them is being 3.5 cm and total height of solid 9.5 cm. Find volume of the solid ?
Solution