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Solution - A Tent Consists of a Frustum of a Cone Capped by a Cone. If the Radii of the Ends of the Frustum Be 13 M and 7 M , the Height of the Frustum Be 8 M and the Slant Height of the Conical Cap Be 12 M, Find the Canvas Required for the Tent. (Take : π = 22/7) - CBSE Class 10 - Mathematics

Question

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)

Solution

The height of the frustum cone is h= 8 m. The radii of the end circles of the frustum are r1 = 13m and r2 =7m.

The slant height of the frustum cone is

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

`=sqrt((13-7)^2+8^2`

`=sqrt(100)`

= 10 meter

The curved surface area of the frustum is

`S_1=pi(r_1+r_2)xxl`

= π x (13+7) x 10

= π 20 x 10

= 200π m2

The base-radius of the upper cap cone is 7m and the slant height is 12m. Therefore, the curved surface area of the upper cap cone is

S= π x 7 x 12

`=22/7xx7xx12`

= 22 x 12

= 264 m2

Hence, the total canvas required for the tent is

S1 + S2 = 200π + 264

= 892.57 m2

 Hence total canvas is 892.57 m2

 

  Is there an error in this question or solution?

APPEARS IN

 R.D. Sharma 10 Mathematics (with solutions)
Chapter 16: Surface Areas and Volumes
Q: 9

Reference Material

Solution for question: A Tent Consists of a Frustum of a Cone Capped by a Cone. If the Radii of the Ends of the Frustum Be 13 M and 7 M , the Height of the Frustum Be 8 M and the Slant Height of the Conical Cap Be 12 M, Find the Canvas Required for the Tent. (Take : π = 22/7) concept: Surface Area of a Combination of Solids. For the course CBSE
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