NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.7 – Part 4

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Surface area of cone= πrl

Surface Area of Cone

Surface area of cone= πrl

Q-8 If the triangle BEC in the Question 7 above is revolved about the side 5 cm, and then fined the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.If the triangle is revolved about the side of 5 cm then the 12 cm side becomes the radius of the cylinder and the 13 cm side remains the slant height.

Solution:

Triangle BEC Rotated to Form a Cone

Triangle BEC, the side 5cm

Given, a right circular cone with

  • Radius

  • Height

Therefore, volume

Now, from previous problem, the right circular cone base is and height

Therefore, volume

Ratio of the volumes = or

Q-9 A heap of wheat is in the form of a cone whose diameter is and height is Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

Solution:Given,

  • Diameter of the base of the cone

  • Radius

  • Height of the cone

Volume of the heap is

Also to calculate the slant height,

Area of canvas = Curved surface area of the cone

  • That is,

  • (approx.)