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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? - CBSE Class 10 - Mathematics

ConceptSurface Areas and Volumes Examples and Solutions

#### 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

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

#### Reference Material

Solution for 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? concept: Surface Areas and Volumes Examples and Solutions. For the course CBSE
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