the radii of the ends of the frustumof a cone 45cm high are 28cm and 7 cm find its - Maths - Surface Areas and Volumes

Question

the radii of the ends of the frustumof a cone 45cm high are 28cm
and 7 cm find its volume , the C S A & the T S A

Ajanta Trivedi · Accepted Answer

let the height of the frustum be h=45 cm let the radius of the base be r=7 cm

its largerer radius be R=28 cm volume of the frustum= $\frac{π h}{3} (R^{2} + R r + r^{2}) = \frac{22}{7} * \frac{45}{3} (28^{2} + 28 * 7 + 7^{2})$ $= \frac{22}{7} * 15 \cdot (7^{2}) \cdot (16 + 4 + 1) = 2310 * 21 = 48510 c m^{3}$ slant height of the frustum l = $\sqrt{(R - r)^{2} + h^{2}} = \sqrt{(28 - 7)^{2} + 45^{2}} = \sqrt{21^{2} + 45^{2}} = \sqrt{441 + 2025}$ l= $\sqrt{2466} = 49 66 c m$ curved surface area of the frustum= $π (R + r) l = \frac{22}{7} \cdot (28 + 7) * 49 66 = \frac{22}{7} * 35 * 49 66$ CSA=5462 6 cm square total surface area= curved surface area+area of the base+area of the top $= C S A + π r^{2} + π R^{2} = 5462 6 + \frac{22}{7} * 7 * 7 + \frac{22}{7} * 28 * 28 = 5462 6 + 154 + 2464 = 8080 60 c m^{2}$

the radii of the ends of the frustumof a cone 45cm high are 28cm and 7 cm. find its volume , the C.S.A & the T.S.A.