The radius and the height of a cylinder are 2 | vedclass

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Question

(A) The article consists of a cylinder,a hemisphere,and a cone.Radius of cylinder $(r)$ = $28 \, cm$,Height of cylinder $(h_1)$ = $54.5 \, cm$.Radius

Vedclass · Accepted Answer

$17600$

Vedclass · Answer

(A) The article consists of a cylinder,a hemisphere,and a cone.Radius of cylinder $(r)$ = $28 \, cm$,Height of cylinder $(h_1)$ = $54.5 \, cm$.Radius of hemisphere $(r)$ = $28 \, cm$.Radius of cone $(r)$ = $28 \, cm$,Height of cone $(h_2)$ = $21 \, cm$.Slant height of cone $(l)$ = $\sqrt{r^2 + h_2^2} = \sqrt{28^2 + 21^2} = \sqrt{784 + 441} = \sqrt{1225} = 35 \, cm$.The total surface area is the sum of the curved surface area of the cylinder,the curved surface area of the hemisphere,and the curved surface area of the cone.Total Surface Area = $2\pi rh_1 + 2\pi r^2 + \pi rl$.Total Surface Area = $\pi r (2h_1 + 2r + l) = \frac{22}{7} 	imes 28 	imes (2 	imes 54.5 + 2 	imes 28 + 35)$.Total Surface Area = $22 	imes 4 	imes (109 + 56 + 35) = 88 	imes 200 = 17600 \, cm^2$.

The radius and the height of a cylinder are $28 \, cm$ and $54.5 \, cm$ respectively. It is closed at one end by a hemisphere and at the other end by a $21 \, cm$ high cone. Find the total surface area of the combined article. (in $cm^2$)

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