Question

The given figure is a combined solid made up of a cylinder and a
cone. The radius of the base of the solid object is 7cm, length of
the cylindrical part is 35 cm, and the total length of the solid
object is 59cm. Find the total surface area of the solid object
(Ans: 2244cm)


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Answer 1

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Cone:-

r = 7 cm

h = Total height - height of cylinder = 59 - 35 = 24 cm

$l = \sqrt{ {r}^{2} + {h}^{2} } = \sqrt{ {7}^{2} + {35}^{2} }$

$\sqrt{49 + 1225} = 7 \sqrt{26}$

Cylinder:-

r = 7 cm

H = 35 cm

TSA of the solid = TSA of cone + CSA of cylinder + base area of cylinder

= πr(l+r) + 2πrH - πr²

= πr(l+r+2h-r)

= π x 7(7√26 + 7 + 2 x 35 - 7)

= 7π (7√26 + 70)

= 49π(√26+10)

= 154(√26+10) cm²