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Solution for A Solid is in the Shape of a Frustum of a Cone. the Diameter of Two Circular Ends Are 60cm and 36cm and Height is 9cm. Find Area of Its Whole Surface and Volume? - CBSE Class 10 - Mathematics

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Question

A solid is in the shape of a frustum of a cone. The diameter of two circular ends are 60cm and 36cm and height is 9cm. find area of its whole surface and volume?

Solution

Given that,

The radii of the upper and lower circle of the frustum of the cone are r1 = 30 cm and r2 = 18 cm respectively

the height of the frustum of a cone h =9 cm.

The slant height of the cone

`l=sqrt(h^2+(r_1-r_2)^2)`

`=sqrt(9^2+(30-18)^2`

`=sqrt(81+144)`

`=sqrt(225)`

= 15 cm

The volume of the frustum cone 

`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`

`=1/3pi(30^2+30xx18+18^2)xx9`

`=1/3pi(900+540+324)xx9`

`=1/3pixx1764xx9`

= π x 1764 x3

=  5292π cm3

Hence, volume of the frustum cone is 5292π cm3

The total surface narea of the frustum cone

`S=pi(r_1+r_2)xxl+pi r_1^2+pir_2^2`

   = π (30+18) x 15 + π x 302 + π x 182 

 = π (48 x 15) + 900 π + 324 π

 = 720π + 900π + 324π

 = 1944π cm2

Hence, the total surface area of the freustum cone is 1944π cm

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Q: 16

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Solution A Solid is in the Shape of a Frustum of a Cone. the Diameter of Two Circular Ends Are 60cm and 36cm and Height is 9cm. Find Area of Its Whole Surface and Volume? Concept: Surface Areas and Volumes Examples and Solutions.
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