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

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 Equation and Equation respectively. Find the cost of white-washing its curved surface at the rate of Equation per Equation Solution:

We know,

  • Base diameter = Equation

  • Radius (r) Equation

  • Slant height of tomb (l) Equation

Therefore curved surface area = Equation Equation

Rate of white- washing 100 m2 Equation

Rate of white- washing 1 m2 Equation

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

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

  • The cone radius (r) Equation

  • The cone height (h) Equation

Now, l be the slant height

  • Equation

  • Equation

  • Equation

  • Equation

Sheet required for one cap = Curved surface of the cone

  • Equation

  • Equation

  • Equation

Sheet required for Equation

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

Solution:

We are given,

  • Radius of the cone (r) Equation

  • Height of the cone (h) Equation

Now, the slant height of a cone Equation is given by

  • Equation

  • Equation

  • Equation

  • Equation

We know that, rate of painting Equation

Curved surface area of 1 cone Equation = Equation

Therefore, curved surface of such 50 cones = Equation

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

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