NCERT Solutions For Class 9 Math | Exer 13.3

Exercise 13.3 of class 9 NCERT math text book comprises 8 questions. This exercise focuses on curved surface area and total surface area of right circular cones. Video solutions have been provided for the tougher questions - question 5 and question 8.

How to find the Curved Surface Area of Cone? What is the formula for Curved Surface Area of a Ccone?

The formula to compute the curved surface area of cone is πrl, where 'r' is the radius of the base of the right circular cone and 'l' is the slant height. It is also known as the lateral surface area of the cone.

The slant height of the cone, l = \\sqrt{h^2 + r^2}), where 'r' is the radius of the cone and 'h' is the height of the cone.

How to find the Total Surface Area of Cone (TSA)? What is the formula to find the Total Surface Area of cone?

The total surface area of cone is the sum of the curved surface area of cone and the area of the circular base of the cone.

i.e., TSA of cone = CSA + Area of circular base = πrl + πr²

The formula to compute the total surface area of cone is πr(r + l), where 'r' is the base radius of the right circular cone and 'l' is the slant height of the right circular cone.

1. Question 1

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

   Explanation

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2. Question 2

   Find the total surface area of the cone, if its slant height is 21 m and diameter of its base is 24 m.

   Explanation

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3. Question 3

   Curved surface area of the 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

   Explanation

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4. Question 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 1 m² canvas is Rs.70.

   Explanation

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5. Question 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 the extra length of the material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14).

   Explanation Video Solution

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6. Question 6

   The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs.210 per 100 m².

   Explanation

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7. Question 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.

   Explanation

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8. Question 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 the painting is Rs.12 per m², what will be the cost of painting all these cones? (Use π = 3.14 and take √1.04 = 1.02)

   Explanation Video Solution

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Exercise 13.1 | Surface Area of Cubes & Cuboids

1. Class 9 Exercise 13.1 Question 3 | Height of hall ▶
2. Class 9 Exercise 13.1 Question 6 | TSA of Herbarium ▶
3. Class 9 Exercise 13.1 Question 7 | Shanti Sweets ▶

Exercise 13.2 | Surface Area of Cylinders

1. Class 9 Exercise 13.2 Question 3 | CSA TSA of Metal Pipe ▶
2. Class 9 Exercise 13.2 Question 4 | Roller & Playground ▶
3. Class 9 Exercise 13.2 Question 9 | Cylindrical Petrol Tank ▶
4. Class 9 Exercise 13.2 Question 10 | CSA of Decorative Lampshade ▶

Exercise 13.3 | Surface Area of Cones

1. Class 9 Exercise 13.3 Question 5 | Length of Tarpaulin 3 m wide ▶
2. Class 9 Exercise 13.3 Question 8 | Cost of painting conical barricades ▶

Exercise 13.4 | Surface Area of Spheres & Hemispheres

1. Class 9 Exercise 13.4 Question 8 | Outer CSA of hemispherical bowl ▶
2. Class 9 Exercise 13.4 Question 9 | Surface area of sphere & Cylinder ▶