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# NCERT Solutions for Class 10 Maths Exercise 13.3

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NCERT solutions for Maths Surface Areas and Volumes

## NCERT Solutions for Class 10 Maths Surface Areas and Volumes

###### 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 = 2.74 cm

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 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

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 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

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

= 2.5 m

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 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

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 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, Diameter = 6 cm

Radius = = 3 cm and height = 12 cm

Let cones be filled with ice cream.

Then, According to question,

Volume of cones = Volume of right circular cylinder

=

= 15

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 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

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 7. A cylindrical bucket, 32 cm and 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

Then, Volume =

= =

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

=

= 1296

= 36 cm

Now, Slant height =

= =

= = cm

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 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 = 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

Volume of water that flows in 30 minutes

= =

The area it will irrigate =

=

= hectares = 56.25 hectares

NCERT Solutions for Class 10 Maths Exercise 13.3

###### 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

Volume = = =

Rate of flow of water = 3 km/h = 3000 m/h = m/min = 50 m/min

For pipe, Internal diameter = 20 cm, therefore radius = 10 cm = 0.1 m

Volume of water that flows per minute =

= =

Required time = = 100 minutes

## NCERT Solutions for Class 10 Maths Exercise 13.3

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### 10 thoughts on “NCERT Solutions for Class 10 Maths Exercise 13.3”

1. In 3rd question in finding h portion there is mistake of ×20

2. nice solutions but can you do sone some questions in easy language

3. its very helpful…thnxx for ur guidance

4. 5th question is not right.
According to me.

5. I want to understand maths very easily
Can you help me