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

NCERT Solutions for Class 9 Maths Exercise 13.3 Surface Areas and Volumes will help you clearing your concept on surface area of the cones which is one of three dimensional object used in our daily life like joker’s cap ,conical tomb and other conical structures.NCERT Solutions for Class 9 Maths Exercise 13.3 Surface Areas and Volumes is the most important input study material required to cover all the questions which are going to appear in the maths paper of term 2 CBSE Board exam.These NCERT Solutions for Class 9 Maths Exercise 13.3 Surface Areas and Volumes are created by an experienced CBSE teacher by a step by step method for the convenience of the students of class 9.

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**NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes (Term 2 )CBSE Board exam**

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

**Q1.Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area (Assume π=22/7)**

Ans.Diameter of the base of the cone 10.5 cm

Radius of the base,r =10.5/2 = 5.25 cm

The slant height of the cone is,l = 10 cm

Curved surface area of the cone,CSA = ?

CSA = πrl

= (22/7)×5.25×10

= 22 ×0.75 ×10

=22× 7.5

=165 cm²

**Hence Curved surface area of the cone is 165 cm²**

**Q2.Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m. (Assume π = 22/7)**

Ans. The slant height of the cone is,l = 21 cm

Diameter of the base of the cone= 24 cm

Radius of the base,r =24/2 = 12cm

**Total surface area of the cone,TSA =πr(r +l)**

TSA = (22/7)×12(12 +21)

= (22/7)×12×33

= 1244.57 cm²

**Hence total surface area of the cone is 1244.57 cm²**

**Q3.Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find**

**(i) radius of the base and (ii) total surface area of the cone.**

**(Assume π = 22/7)**

Ans.Curved surface area of a cone .CSA= 308 cm²

The slant height of the cone is,l = 14 cm

(i) CSA of the cone = πrl

(22/7)×r×14 = 308

r = (308×7)/(22×14)

= (14×7)/14

= 7 cm

**Hence** **radius of the base is 7 cm**

**Q4.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 1 m ^{2} canvas is Rs 70.**

**(Assume π=22/7)**

Ans. The height(h) of the conical tent = 10 m

Radius of its base,r = 24 m

(i)Let slant height of the conical tent is =l

Applying Pythogorus theorem

l = r² + h²

l = √(r² + h²)

= √(24² + 10²)

=√(576 + 100)

=√676 = 26

**Hence slant height of the conical tent is 26 m**

(ii)Cost of 1 m^{2} canvas is Rs 70

The canvas required to make the tent = curve surface area of the tent

∴The canvas required to make the tent

=πrl

=(22/7)×24×26

=13728/7

Therefore canvas required to make the tent is 13728/7 m²

Cost of the canvas required to make the tent = cost of 1m² canvas ×canvas required to make the tent

= 70 ×13728/7

=10 ×13728 = 137280

**Hence the cost of the canvas required to make the tent is Rs 137280**

**Q5.What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π=3.14]**

Ans.Let the length of tarpaulin required to make conical tent is x

Breadh of tarpaulin is given 3 m

Height(h) of the conical tent is given 8 m and radius(r) 6 m

Slant height(l) = √(8² +6²) = √(64 +36)=√100 = 10 m

The extra length of material that will be required for stitching margins and wastage in cutting is given 20 cm=0.20 m

Curved surface area of the conical tent is = πrl

Area of the tarpaoline = Length × Breadh

Since 0.20 m of the length is used for stitching margins and wastage

∴ (Length +0.20)× Breadh = πrl

(x -0.20)3 = (22/7) ×6×10

7(3x – 0.60 )= 22×6×10

21x – 4.20 = 1320

21x = 1320 +4.20

21x = 1320

x = 1320/21 =62.89≈63

**Hence the length of the tarpauline required to make conical tent is 63 m**

**Q6.The slant height and base diameter of conical tomb are 25m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs. 210 per 100 m ^{2}. (Assume π = 22/7)**

Ans. The given dimensions of conical tomb are given as following

The slant height of the conical tomb is,l = 25 m

Diameter of the base of the conical tomb= 14 m

Radius of the base,r =14/2 = 7m

Curved surface area of the conical tomb

=πrl

=(22/7)×7×25

=22×25 =550

**Hence the curved surface area of the conical tent is 550 m²**

The cost of whitewashing its curved surface area is Rs 210 per 100 m²

The cost of whitewashing in 1 m² = 210 /100

The cost of whitewashing the curved surface area of the tomb

= 550 ×(210 /100)

=55×21 =1155

**Hence the cost of white-washing curved surface area of the tomb is Rs 1155**

**Q7.A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24cm. Find the area of the sheet required to make 10 such caps. (Assume π =22/7)**

Ans.The given dimensions of joker’s cap are given as following

The height of the joker’s cap is,h = 24cm

Radius of the base,r = 7cm

The height of the joker’s cap is,h = 24cm

Slant height(l) = √(24² +7²) = √(576 +49)=√625 = 25 cm

Curved surface area of the joker’s cap

=πrl

=(22/7)×7×25 = 550

Hence the curved surface area of the joker’s cap is 550 cm²

**The area of the sheet required to make 10 such caps = 10× 550 =5500 cm²**

**Q8.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? (Use π = 3.14 and take √(1.04) =1.02)**

Ans. The base diaeter of the hollow cone is 40 cm,therefore radius(r) is 20 cm=0.20m

Height of the hollow cone is given 1m

Slant height of the hollow cone , l = √(0.20² +1²) = √(0.04 +1)=√1.04= 1.02 m

Curved surface area of the hollow cone

=πrl

=3.14×0.20×1.02 = 0.64056

The curved surface area of single hollow cone is 0.64056 m²

The curved surface area of 50 hollow cone is 0.64056 ×50=32.028 m²

Cost of painting is Rs. 12 per m²

**The cost of painting all these cones is = 12×32.028 =384.336≈Rs 384.34**

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