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# Solution - A Frustum of a Right Circular Cone Has a Diameter of Base 20 Cm, of Top 12 Cm, and Height 3 Cm. Find the Area of Its Whole Surface and Volume. - CBSE Class 10 - Mathematics

ConceptSurface Area of a Combination of Solids

#### Question

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

#### Solution

The radii of the bottom and top circles are r1 = 10 cm and r2 = 6 cm respectively. The height of the frustum cone is h= 3 cm. Therefore, the volume of the bucket is

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

=1/3pi(10^2+10xx6+6^2)xx3

= 616 cm3

Hence Volume = 616 cm3

The slant height of the bucket is

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

=sqrt((10-6)^2+3^2)

=sqrt(25)

= 5cm

The total surface area of the frustum cone is

pi(r_1+r_2)xxl+pir_1_pir_2^2

=22/7xx(10+6)xx5+22/7xx10^2+22/7xx6^2

=4752/7Square cm

= 678.85 Square cm

Hence Total surface area = 678.85

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: 2

#### Reference Material

Solution for question: A Frustum of a Right Circular Cone Has a Diameter of Base 20 Cm, of Top 12 Cm, and Height 3 Cm. Find the Area of Its Whole Surface and Volume. concept: Surface Area of a Combination of Solids. For the course CBSE
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