Question

The radii of the circular ends of a frustum of a solid cone are 20 cm and 12 cm and its
height is 6 cm, then find the volume and the surface area of the frustum.​

Answer 1

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Answer 2

Surface area of the frustum = 2715.43 cm²

Volume of the frustum = 4928 cm³

Step-by-step explanation:

Radii of the circular ends of the frustum of a solid cone are 20 cm and 12 cm respectively.

Height of the frustum is 6 cm.

Since volume of the frustum is defined by the formula,

V = $\frac{1}{3}\pi h(r^{2}+R^{2}+rR)$

  = $\frac{1}{3}\pi 6[12^{2}+20^{2}+(12)(20)]$

  = 2π(144 + 400 + 240)

  = 2π(784)

  = 4928 cm³

Surface area of the frustum = $\pi (r+R)\sqrt{(R-r)^{2}+h^{2}}+\pi r^{2}+\pi R^{2}$

= $\pi (20+12)\sqrt{(20-12)^{2}+6^{2}}+\pi (12^{2})+\pi (20^{2})$

= $\pi (32)\sqrt{100}+\pi (144+400)$

= $\pi [(320)+(544)]$

= $\pi (864)$

= 2715.43 cm²

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