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Question
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is `14/3` m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.
Solution
Given that:
Radius of the same base `r=3.5/2=1.75 m`
Height of the cylinder `h=14/3m`
The volume of the vessel is given by
`V=pir^2h+2/3pir^3`
`=3.14xx1.75^2xx14/3+2/3xx3.14xx1.75^3`
= 56 m3
The internal surface area of the solid is
`S=2pir^2+2pirh`
`=2xx3.14xx1.75^2+2xx3.14xx1.75xx14/3`
= 70.51 m2
Hence, the volume of the vessel and internal surface area of the solid is V = 56 m3, S= 70.51 m2
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Assertion (A)
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A surahi is the combination of ______.
There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 66 cm long and he takes exactly 400 steps to go around the pond, find the diameter of the pond.
