Question

a cylinder with radius 6 centimetre is closed at one end by a 8cm high cone and is open at the other and the total height of the articles 20 centimetre find the total surface area of the article ​

Answer 1

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Answer 2

GIVEN :

• A CYLINDER IS CLOSED AT ONE END BY A CONE
• RADIUS OF CYLINDER = 6 cm
• HEIGHT OF CONE = 8 cm
• TOTAL HEIGHT = 20 cm

TO FIND :

1. TOTAL SURFACE AREA (TSA) OF ARTICLE

SOLUTION :

RADIUS OF CYLINDER = RADIUS OF CONE

=> RADIUS OF CONE = 6 cm

LET SLANT HEIGHT OF CONE BE 'l '

IN A CONE ,

$l {}^{2} = {r}^{2} + {h}^{2} \\ \\ = > {l}^{2} = 36 \: + 64 \: \: = > {l}^{2} = 100 \\ \\ = > l = 10cm$

TOTAL HEIGHT OF ARTICLE = HEIGHT OF CONE + HEIGHT OF CYLINDER

=> 20 = 8 + HEIGHT OF CYLINDER

=> HEIGHT OF CYLINDER = 12 cm

TSA OF ARTICLE = TSA OF CONE + TSA OF CYLINDER

$= > tsa \: of \: article = \pi r(l + r) + 2\pi r(r + h) \\ \\ = 6\pi(16) + 12\pi(18) \\ \\ = 96\pi + 216\pi = 312\pi = 980.57 {cm}^{2}$

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