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Install NowNCERT Solutions for Class 10 Maths Exercise 13.1 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 10 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.
NCERT solutions for Maths Surface Areas and Volumes Download as PDF
NCERT Solutions for Class 10 Maths Surface Areas and Volumes
Unless stated otherwise, take 
1. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Ans. Volume of cube = 
According to question, = 64
Side = 4 cm
For the resulting cubiod, length 
= 4 + 4 = 8 cm, breadth 
= 4 cm and height 
= 4 cm
Surface area of resulting cuboid = 
= 
= 2 (32 + 16 + 32)
= 
NCERT Solutions for Class 10 Maths Exercise 13.1
2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Ans. 
Diameter of the hollow hemisphere = 14 cm
Radius of the hollow hemisphere = 
= 7 cm
Total height of the vessel = 13 cm
Height of the hollow cylinder = 13 – 7 = 6 cm
Inner surface area of the vessel
= Inner surface area of the hollow hemisphere + Inner surface area of the hollow cylinder
= 
= 
= 
= 
NCERT Solutions for Class 10 Maths Exercise 13.1
3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Ans. Radius of the cone = 3.5 cm
Radius of the hemisphere = 3.5 cm
Total height of the toy = 15.5 cm
Height of the cone = 15.5 – 3.5 = 12 cm
Slant height of the cone = 
= 
= 
= 12.5 cm
TSA of the toy = CSA of hemisphere + CSA of cone
= 
= 
= 
= 
= 
= 
NCERT Solutions for Class 10 Maths Exercise 13.1
4. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
Ans. Greatest diameter of the hemisphere = Side of the cubical block = 7 cm
TSA of the solid = External surface area of the cubical block + CSA of hemisphere
= 
= 
= 
= 
= 
= 294 + 38.5 = 
NCERT Solutions for Class 10 Maths Exercise 13.1
5. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter 
of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Ans. Diameter of the hemisphere = , therefore radius of the hemisphere = 
Also, length of the edge of the cube =
Surface area of the remaining solid
= 
= 
= 
= 
NCERT Solutions for Class 10 Maths Exercise 13.1
6. 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
= 
= 
= 
= 
= 
NCERT Solutions for Class 10 Maths Exercise 13.1
7. 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
. (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
= 
= 
= 
= 
= 
Cost of the canvas of the tent at the rate of Rs. 500 per 
= 
= Rs. 22000
NCERT Solutions for Class 10 Maths Exercise 13.1
8. 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
.
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
= 
(to the nearest )
NCERT Solutions for Class 10 Maths Exercise 13.1
9. 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 = 
= 
= 
= 
= 
= 
NCERT Solutions for Class 10 Maths Exercise 13.1
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Class 10 Science MCQ