Question

a wooden article was made by scooping out . A hemisphere from each ends of solid hemisphere . if the height of a cylinder 10cm . it base of radius 3.5 cm . find T.S.A of article

Answer 1

⋆ Reference of image is shown in diagram

$\setlength{\unitlength}{1.5 cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,0.7)(2,0)\qbezier(0,0)(1.1,1.7)(2,0)\qbezier(0,0)( 1, - 0.7)(2,0)\put(2.3,1){\vector(0,1){1.5}}\put(2.3,1){\vector(0, - 1){1.2}}\put(2.3,1){ \bf h }\put(0.3,0.1){ \bf r }\put(0,0){\vector(1,0){1}}\qbezier(0,2.5)(1,1.8)(2,2.5)\qbezier(0,2.5)(1.1,0.7)(2,2.5)\qbezier(0,2.5)(1, 3.2)(2,2.5)\end{picture}$

⠀⠀⠀⠀⠀⠀⠀☯ Let r be the radius of the base of the cylinder and h be it's height. Let S be the total surface area of the article.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

S = Curved surface area of the cylinder + 2(Surface area of a hemisphere)

$\qquad \quad:\implies\sf \pink{S = 2\pi rh + 2(2 \pi r^2)}$

$\qquad \qquad:\implies\sf S = 2 \pi r(h + 2r)$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━

$\sf Here \begin{cases} & \sf{Radius,\;r = 3.5\;cm } \\ & \sf{Height,\;h = 10\;cm} \end{cases}$

$\star\;{\underline{\frak{Putting\;values\;:}}}$

$:\implies\sf S = 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{3.5} \bigg\lgroup\sf 10 + 2 \times 3.5) \bigg\rgroup$

$\quad \: :\implies\sf S = 2 \times 22 \times 0.5\bigg\lgroup\sf 10 + 7 \bigg\rgroup$

$\qquad \: \: \: \: :\implies\sf S = 44 \times 0.5\bigg\lgroup\sf 17 \bigg\rgroup$

$\qquad \qquad:\implies\sf S = 44 \times 8.5$

$\qquad \qquad:\implies{\boxed{\frak{\purple{S = 374\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Total\; surface\;area\;of\;cylinder\;is\; \bf{374\;cm^2}.}}}$