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# 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. - Mathematics

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#### 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

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 14: Surface Areas and Volumes
Ex. 14.3 | Q: 2 | Page no. 78

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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. Concept: Surface Area of a Combination of Solids.
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