NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.3 – Part 3

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Surface area and volume of a cone

Surface Area and Volume of a Cone

Surface area and volume of a cone

Q-6 The slant height and base diameter of a conical tomb are and respectively. Find the cost of white-washing its curved surface at the rate of per Solution:

We know,

  • Base diameter =

  • Radius (r)

  • Slant height of tomb (l)

Therefore curved surface area =

Rate of white- washing 100 m2

Rate of white- washing 1 m2

Therefore, total cost of white-washing the tomb with area

Q-7 A joker’s cap is in the form of a right circular cone of base radius and height . Find the area of the sheet required to make such caps.Solution:

  • The cone radius (r)

  • The cone height (h)

Now, l be the slant height

Sheet required for one cap = Curved surface of the cone

Sheet required for

Q-8 A bus stop is barricaded from the remaining part of the road, by using hollow cones made of recycled cardboard. Each cone has a base diameter of and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is , what will be the cost of painting all these cones? (Use and take )

Solution:

We are given,

  • Radius of the cone (r)

  • Height of the cone (h)

Now, the slant height of a cone is given by

We know that, rate of painting

Curved surface area of 1 cone =

Therefore, curved surface of such 50 cones =

Finally, cost of painting all these cones is (since, the cost of painting is )