Q. 64.0( 6 Votes )

# The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm, and its slant height is 10 cm. Find its capacity and total surface area. [Take π = 22/7.]

Answer :

Given: Radius of lower circular end = r = 27 cm

Radius of upper circular end = R = 33 cm

Slant height = l = 10cm

Total surface area of frustum = πr^{2} + πR^{2} + π(R + r)l cm^{2}

Here h height of frustum is not given and we need h to find the volume of frustum therefore we must first calculate the value of h as follows

using formula for slant height and with the help of given data we get

Squaring both sides

∴ 100 = 36 + h^{2}

∴ h^{2} = 64

∴ h = 8

As length cannot be negative

∴ h = 8 cm

= 22 × 8 × 129

= 22704 cm^{3}

∴ capacity = volume of frustum = 22704 cm^{3}

Total surface area of frustum = πr^{2} + πR^{2} + π(R + r)l cm^{2}

= (22/7) × (1089 + 729 + 600)

= (22/7) × 2418

= 7599.428 cm^{2}

∴ total surface area = 7599.428 cm^{2}

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