CBSE Class 10 Maths Chapter-13 Surface Areas and Volumes – Free PDF Download
Free PDF download of Important Questions with Answers for CBSE Class 10 Maths Chapter 13 – Surface Areas and Volumes prepared by expert Maths teachers from latest edition of CBSE(NCERT) books only by CoolGyan to score more marks in CBSE board examination.
CBSE Class 10 Maths Chapter-13 Surface Areas and Volumes Important Questions
CBSE Class 10 Maths Important Questions Chapter 13 – Surface Areas and Volumes
4 Mark Questions
1. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Ans. Radius of the hemisphere = 
mm
Let radius = 
= 2.5 mm
Cylindrical height = Total height – Diameter of sphere = 
= 14 – (2.5 + 2.5) = 9 mm
Surface area of the capsule = CSA of cylinder + Surface area of the hemisphere
= 
= 
= 
= 
= 220 mm2
2. A tent is in the shape of a cylinder surmounted buy a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per m2. (Note that the base of the tent will not be covered with canvas.)
Ans. Diameter of the cylindrical part = 4 cm
Radius of the cylindrical part = 2 cm
TSA of the tent = CSA of the cylindrical part + CSA of conical cap
= 
= 
= 
= 
= 44 m2
Cost of the canvas of the tent at the rate of Rs. 500 per m2
= 44 x 500 = Rs. 22000
3. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
Ans. Diameter of the solid cylinder = 1.4 cm
Radius of the solid cylinder = 0.7 cm
Radius of the base of the conical cavity = 0.7 cm
Height of the solid cylinder = 2.4 cm
Height of the conical cavity = 2.4 cm
Slant height of the conical cavity = 
= 
= 
= 2.5 cm
TSA of remaining solid
= 
= 
= 
= 
= 17.6 cm2
= 18 cm2 (to the nearest cm2)
4. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.
Ans. TSA of the article = 
= 
= 
= 
= 
= 374 cm2
5. Derive the formula for the curved surface area and total surface area of the frustum of a cone, given to you in Section 13.5, using the symbols as explained.
Ans. According to the question, the frustum if difference of the two cones OAB and OCD (in figure).
For frustum, height = 
slant height = 
and radii of the bases = 
and 
OP = 
OA = OB =
Height of the cone = 
OQD
OPB [AA similarity]
……….(i)
height of the cone OCD =
= 
= 
……….(ii)
V of the frustum = V of cone OAB – V of cone OCD
= 
= 
[From eq. (i) & (ii)]
= 
= 
If A1 and A2 are the surface areas of two circular bases, then
A1 = 
and A2 = 
V of the frustum = 
= 
Again, from DEB, 
OQDOPB [AA similarity]
……….(iii)
= 
……….(iv)
Hence, CSA of the frustum of the cone = 
= 
[From eq. (i) and (ii)]
= 
= 
, where
TSA of the frustum of the cone = 
6. A bucket made up of metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which will completely fill the bucket at the rate Rs. 20 per litre and cost of metal sheet used if it costs Rs. 10 per 100 cm2.
Ans. 
(i) Volume of bucket 
Quantity of milk =
litres
Cost of 1 litre of milk = Rs.20
Cost of 8.164 litres milk = Rs. 20 × 8.14
=Rs. 163.28
(ii) T.S.A. of bucket (excluding the upper end)
Cost of 100 cm2 metal sheet = Rs.10
Cost of 1711.3 cm2 metal sheet = 
7. A solid consisting of a right circular cone standing on a hemisphere, is placed upright in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder having given that the radius of the cylinder is 3cm and its height is 6cm. The radius of hemisphere is 2cm and the height of the cone is 4cm. Give your answer to the nearest cubic centimeters.
Ans. Volume of cylinder = 
Volume of cone 
Volume of hemisphere 
Volume of water in the cylinder
8. A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in his field which is 10m in diameter and 2m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Ans. Rate of water flowing = 
In 1 second the water flows = 
Internal diameter = 
Volume of the water that flows through the pipe in one second = 
Volume of water in the tank = 
Time taken to fill the tank = 
seconds
= 100 minutes = 1hour 40 minutes
9. A cone of radius 10cm divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volume of the two parts.
Ans. Let OAB be the cone and OQ be its axis and P be the mid-point of OQ
Let OQ = h cm
Then 
And QB = 10cm
Also 
(i) A smaller cone of radius = 5cm and height = h/2cm
(ii) Frustum of a cone in which
Volume of smaller cone = 
Volume of frustum of the cone 
Ratio of required volume 
