NCERT Solutions for Class 10 Maths Exercise 13.5

NCERT Solutions for Class 10 Maths Exercise 13.5 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

1. A copper wire, 3 mm in diameter is wound about a cylinder whose length is 12 cm and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per.

Ans. Number of rounds to cover 12 cm, i.e. 120 mm = = 40

Here, Diameter = 10 cm, Radius cm

Length of the wire in completing one round

= cm

Length of the wire in completing 40 rounds

= cm

Radius of the copper wire = mm

= cm

Volume of wire =

=

Mass of the wire =

= 787.98 g

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NCERT Solutions for Class 10 Maths Exercise 13.5

2. A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of as found appropriate)

Ans. Hypotenuse = = 5 cm

In figure, ADB CAB [AA similarity]

AD = cm

Also,

DB = cm

CD = BC – DB = cm

Volume of the double cone

=

= =

Surface area of the double cone

=

= =

=

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NCERT Solutions for Class 10 Maths Exercise 13.5

3. A cistern, internally measuring has 129600 of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being?

Ans. Volume of cistern = =

Volume of water =

Volume of cistern to be filled

= 1980000 – 129600 =

Volume of a brick =

=

Let bricks be needed.

Then, water absorbed by bricks =

= 1792 (approx.)

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NCERT Solutions for Class 10 Maths Exercise 13.5

4. In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

Ans. Volume of rainfall =

=

Volume of three rivers =

=

Hence, the two are not approximately equivalent.

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NCERT Solutions for Class 10 Maths Exercise 13.5

5. An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see figure).

Ans. Slant height of the frustum of the cone

= = 13 cm

Area of the tin sheet required

= CSA of cylinder + CSA of the frustum

=

=

= = =

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NCERT Solutions for Class 10 Maths Exercise 13.5

6. 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)]

=

=

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NCERT Solutions for Class 10 Maths Exercise 13.5

7. Derive the formula for the volume for the volume of the frustum of a cone, given to you in Section 13.5, using the symbols as explained.

Ans. If are the surface areas of two circular bases, then

A₁ = and A₂ =

V of the frustum

=

=

Again, from DEB,

OQD OPB [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

=

NCERT Solutions for Class 10 Maths Exercise 13.5

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