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the perimeter of the circular base of a cone is 132 cm and its vertical height is 28 cm find the curved surface area total surface area and volume of the cone​

User Cagatay
by
8.5k points

1 Answer

9 votes

Answer:

i. Curved surface area = 2310
cm^(2)

ii. Total surface area = 3696
cm^(2)

iii. volume = 12936
cm^(3)

Explanation:

Perimeter of the circular base = circumference of the circle = 132 cm

circumference of a circle = 2
\pir

132 = 2
\pir

r =
(132)/(2\pi )

=
(66)/(\pi )

r = 66 x
(7)/(22)

= 3 x 7

= 21

radius = 21 cm

vertical height, h = 28 cm

Thus applying the Pythagoras theorem,


l^(2) =
h^(2) +
r^(2)

=
28^(2) +
21^(2)

= 784 + 441

= 1225

l =
√(1225)

l = 35 cm

The slant height is 35 cm.

i. Curved surface area =
\pirl

=
(22)/(7) x 21 x 35

= 22 x 3 x 35

= 2310

curved surface area of the cone is 2310
cm^(2).

ii. Total surface area =
\pi r^(2) +
\pirl

=
\pir(r + l)

=
(22)/(7) x 21 (21 + 35)

= 22 x 3 x 56

= 3696

The total surface area of the cone is 3696
cm^(2).

iii. volume of a cone =
(1)/(3)
\pi r^(2)h

=
(1)/(3) x
(22)/(7) x
21^(2) x 28

= 12936

The volume of the cone is 12936
cm^(3)

User Sandun Madola
by
8.2k points

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