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NCERT Solutions for Class 9 Maths Exercise 13.3 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 9 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 Class 9 Maths ****Surface Areas and Volumes ****Download as PDF**

## NCERT Solutions for Class 9 Mathematics Surface Areas and Volumes

**Assume ****unless ^stated otherwise**.

**1. ****Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area and its total surface area.**

**Ans.** Diameter = 10.5 cm

Radius = = cm

Slant height of cone = 10 cm

Curved surface area of cone=

= = 165 cm^{2}

Total surface area of cone =

=

= = 251.625 cm^{2}

**2. Find the total surface area of a cone, if its slant height is 21 cm and diameter of the base is 24 cm.**

**Ans.** Slant height of cone = 21 m

Diameter of cone = 24 m

Radius of cone = = 12 m

Total surface area of cone =

=

= = 1244.57 m^{2}

**3. Curved surface area of a cone is 308 cm**^{2} and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.

^{2}and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.

**Ans. (i)** Slant height of cone = 14 cm

Curved surface area of cone = 308 cm^{2}

= 308

= 7 cm

**(ii)** Total surface area of the cone

= Curved surface area + Area of circular base

=

=

= 462 cm^{2}

NCERT Solutions for Class 9 Maths Exercise 13.3

**4. ****A conical tent is 10 m high and the radius of its base is 24 m. Find:**

**(i) ****slant height of the tent.**

**(ii) ****cost of the canvas required to make the tent, if the cost of a m ^{2} canvas is Rs. 70.**

**Ans.** Height of the conical tent= 10 m

Radius of the conical tent = 24 m

**(i)** Slant height of the tent

=

= = = 26 m

**(ii)** Canvas required to make the tent

= Curved surface area of the tent=

= = m^{2}

Cost of 1 m^{2} canvas = Rs. 70

Cost of m^{2} canvas

= 70 x = Rs. 137280

NCERT Solutions for Class 9 Maths Exercise 13.3

**5. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. **

**Ans.** Height of the conical tent = 8 m and Radius of the conical tent = 6 m

Slant height of the tent

= = = = 10 m

Area of tarpaulin = Curved surface area of tent = = 3.14 x 6 x 10 = 188.4 m^{2}

Width of tarpaulin = 3 m

Let Length of tarpaulin = L

Area of tarpaulin = Length x Breadth

= L x 3 = 3L

Now According to question,

3L = 188.4

L = = 62.8 m

The extra length of the material required for stitching margins and cutting is 20 cm = 0.2 m.

So the total length of tarpaulin bought is (62.8 + 0.2) m = 63 m

NCERT Solutions for Class 9 Maths Exercise 13.3

**6. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of whitewashing its curved surface at the rate of Rs. 210 per 100 m**^{2}.

^{2}.

**Ans. **Slant height of conical tomb

= 25 m, Diameter of tomb = 14 m

Radius of the tomb = 7 m

Curved surface are of tomb =

= = 550 m^{2}

Cost of white washing 100 m^{2}

= Rs. 210

Cost of white washing 1 m^{2} =

Cost of white washing 550 m^{2}

= = Rs. 1155

NCERT Solutions for Class 9 Maths Exercise 13.3

**7. A Joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. **

**Ans.** Radius of cap = 7 cm,

Height of cap = 24 cm

Slant height of the cone

=

= = = 25 cm

Area of sheet required to make a cap

= CSA of cone =

= = 550 cm^{2}

Area of sheet required to make 10 caps = 10 x 550 = 5500 cm^{2}

NCERT Solutions for Class 9 Maths Exercise 13.3

**8. A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. 12 per m**^{2}, what will be the cost of painting all these cones?

^{2}, what will be the cost of painting all these cones?

**Ans.** Diameter of cone = 40 cm

Radius of cone = 20 cm

= m = 0.2 m

Height of cone = 1 m

Slant height of cone

= = m

Curved surface area of cone =

= 3.14 x 0.2 x

= 0.64056 m^{2}

Cost of painting 1 m^{2} of a cone

= Rs. 12

Cost of painting 0.64056 m^{2} of a cone

= 12 x 0.64056= Rs. 7.68672

Cost of painting of 50 such cones

= 50 x 7.68672 = Rs. 384.34 (approx.)

## NCERT Solutions for Class 9 Maths Exercise 13.3

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