Question

If the radii of the circular ends of a frustum of height 6 cm are 15 cm and 7 cm respectively, then find the volume and lateral surface area (curved surface area) of the frustum

Answer 1

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Answer 2

Given,

The height of the frustum = 6cm

The radii of the frustum = 7cm and  15 cm

To Find,

The volume of the frustum =?

The lateral surface area of the frustum =?

Solution,

The height of the frustum(H) = 6cm

r= 7cm

R = 15cm

From the formula of the slant height(l) of the frustum, we have

$l = \sqrt{H^2 + (r- R)^2} \\l = \sqrt{6^2 + (7- 15)^2} \\l = \sqrt{36 + 8^2} \\l = \sqrt{36 + 64} \\l = \sqrt{100} \\l = 10$

The slant height(l) of the frustum = 10 cm

From the formula of the volume of the frustum, we have

Volume(V) =  πH/3 (R² + Rr + r²)

Volume(V) =  π*6/3 (15² + 15*7 + 7²)

V =  2π (225 + 105 + 49)

V =  2π (225 + 105 + 49)

V = 2π * 379

V = 758π

V = 2382.3 cm³

From the formula of the lateral surface area of the frustum, we have

C.S.A = πl(R + r)

C.S.A = π*10(15 + 7)

C.S.A = π*10*22

C.S.A = 690.8 cm²

Hence, the volume and lateral surface area (curved surface area) of the frustum are 2382.3 cm³ and 690.8 cm² respectively.