NCERT Solutions for Class 10 Maths Exercise 13.3 Chapter 13 Surface Areas and Volumes- FREE PDF Download

NCERT Class 10 Maths Ch 13 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths
Chapter 13 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Surface Areas and Volumes solutions will help you understand the chapter thoroughly.

NCERT Solutions for Class 10 Maths Chapter 13 – Surface Areas and Volumes

Unless stated otherwise, take

1. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Ans. For sphere, Radius

= 4.2 cm

Volume = =

For cylinder, Radius (R) = 6 cm

Let the height of the cylinder be H cm.

Then, Volume = =

According to question, Volume of sphere = Volume of cylinder

H =

H = 2.744 cm

2. Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

Ans. Let the volume of resulting sphere be

cm.

According to question,

= 216 + 512 + 1000

= 1728

= 12 cm

3. A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

Ans. Diameter of well = 7 m

Radius of well = m

And Depth of earth dug = 20 m

Length of platform = 22 m, Breadth of platform = 14 m

Let height of the platform be m

According to question,

Volume of earth dug = Volume of platform

$h^{'} = \frac{22 \times 7 \times 7 \times 20}{28 \times 22 \times 14}$

= 2.5 m

4. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Ans. Diameter of well = 3 m

Radius of well = m and Depth of earth dug = 14 m

Width of the embankment = 4 m

Radius of the well with embankment = m

Let the height of the embankment be m

According to the question,

Volume of embankment = Volume of the earth dug

= 1.125 m

5. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Ans. For right circular cylinder, Diameter = 12 cm

Radius = = 6 cm and height = 15 cm

For cone & Hemisphere , Diameter = 6 cm

Radius = = 3 cm and height = 12 cm

Let cones be filled with ice cream.

Then, According to question,

Volume of (cones +Hemisphere) = Volume of right circular cylinder

$n \times (\frac{1}{3} π {(r_{1}^{})}^{2} (h) + \frac{2}{3} π {(r_{1}^{})}^{3})$ =

$n (\frac{1}{3} π {(3)}^{2} (12) + \frac{2}{3} π {(3)}^{3}) = \frac{22}{7} \times (6)^{2} \times 15$

$n = \frac{22 \times 36 \times 15 \times 3 \times 7}{(7 \times 22 \times 9 \times 12 + 7 \times 44 \times 27)} = \frac{249480}{24948}$

= 10

6. How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions?

Ans. For silver coin, Diameter = 1.75 cm

Radius = cm and Thickness = 2 mm = cm

For cuboid, Length = 5.5 cm, Breadth = 10 cm and Height = 3.5 cm

Let coins be melted.

Then, According to question,

Volume of coins = Volume of cuboid

= 400

7. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Ans. For cylindrical bucket, Radius of the base

= 18 cm and height

= 32 cm

Volume = =

For conical heap, Height = 24 cm

Let the radius be cm.

Then, Volume =

= =

According to question, Volume of bucket = Volume of conical heap

= 1296

= 36 cm

Now, Slant height =

= =

= = cm

8. Water in a canal 6 m wide and 1.5 m deep is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Ans. For canal, Width = 6 m and Depth = 1.5 m =

Speed of flow of water = 10 km/h

= = 10000 m/h

= m/min = m/min

Speed of flow of water in 30 minutes

= m/min = 5000 m/min

Volume of water that flows in 30 minutes

= =

The area it will irrigate =

= hectares = 56.25 hectares

9. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Ans. For cylindrical tank, Diameter = 10 m

Radius = 5 m and Depth = 2 m