Question

the radii of ends of a frustum are 32 cm and 8 cm and the height of frustum of the cone is 54 cm find its volume curved surface area and total surface area

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Answer 1

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Answer 2

Given,

The radii of the frustum are 8cm and 32cm

The height of the frustum(h) = 54cm

To Find,

The volume of the frustum =?

The curved surface area of the frustum =?

The total surface area of the frustum =?

Solution,

r = 8cm

R = 32cm
From the volume of the frustum , we have

V = πH/3 (R² + Rr + r²)

V = π*54/3(64 + 736+256)

V = 18*π(1056)

V = 59685 $cm^{3}$

The slant height = $\sqrt{h^2 + (R - r)^2}$

$l = \sqrt{54^2 + (32 - 8)^2} \\l = \sqrt{2916 + 576} \\l = \sqrt{3492} \\l = 59 cm$

The curved surface area of the frustum = πl(R +r)

The curved surface area of the frustum = π*59*(40)

The curved surface area of the frustum = 9422.1 cm²

The  total surface area of the frustum =  πL (R + r) + π (R² + r²).

The  total surface area of the frustum =  π*59*40 + π*(736 + 64)

The  total surface area of the frustum =  2360π + 800π

The  total surface area of the frustum = 3160π

Hence, the volume, curved surface area, and total surface area is 59685 cm3 , 9422.1 cm² and 3160π cm²