A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner curved surface area of the vessel.

Solution

Let r cm be the radius of the cylinder and h cm be the height of the cylinder, then
r = 7 cm,
and h = (13–7) cm
= 6 cm.
Let r₁ cm be the radius of the hemisphere, then
r₁ = 7 cm
Now,
the inner curved surface area of the vessel
= C,S.A of hemisphere
+ C,S.A of cylinder
= (2πr₁² + 2 π rh) cm²= (2 π r² + 2 π rh) cm² [∵ r₁ = r]
= [2 π r (r + h)] cm²

$equals open square brackets open parentheses 2 space straight x space 22 over 7 space straight x space 7 close parentheses open parentheses 7 space plus space 6 close parentheses close square brackets space cm squared$

= (44 x 13) cm²= 572 cm².

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A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

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A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner curved surface area of the vessel.

Some More Questions From Statistics Chapter

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