Question

the radii of the ends of frustum
of a cone 45cm high are 28cm and 7cm find its volume, the curved surface area and the total surface area ​

Answer 1

Answer:

Let 'ℓ' & R be the radii of the bottom and top circular ends of a frustum of a cone, respectively and 'h' be height of cone.

Volume of the frustum of the cone =

3

1

×

7

22

×45(28

2

+7

2

+28×7)cm

3

=

7

22

×15(784+49+196)cm

3

=

7

22

×15×1029cm

3

=22×15×147cm

3

=330×147cm

3

Now, l=

h

2

+(R−r

2

)

=

(45)

2

+(28−7)

2

=

2025+441

=

2466

=

2466

=49.65cm

curved surface area of the frustum of the cone

=π(R+r)ℓ=[

7

22

∗(28+7)∗49.65]cm

2

=[22×5×49.65]cm

2

5461.5cm

2

total surface area of frustum of the cone

π(R+r)ℓ+πR

2

+πr

2

=[5461.5+

7

22

×(28)

2

+

7

22

×(7)

2

]cm

2

=[5261.5+

7

22

×(28)

2

+(7)

2

]cm

2

=[5461.5+22×1+9]cm

2

=8079.5cm

2