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Home » A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is 4(2/3) m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is 4(2/3) m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.
Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20F | ICSE | Selina
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is 4(2/3) m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(F) - 6

Diameter of the base = 3.5 m

So, its radius = 3.5/2 m = 1.75 m = 7/4 m

Height of cylindrical part = 4 + 2/3 = 14/3

(i)

    \[\begin{array}{*{35}{l}} Capacity\text{ }\left( volume \right)\text{ }of\text{ }the\text{ }vessel\text{ }=\text{ }\pi {{r}^{2}}h\text{ }+\text{ }2/3\text{ }\pi {{r}^{2}}~=\text{ }\pi {{r}^{2~}}\left( h\text{ }+\text{ }2/3r \right) \\ =\text{ }22/7\text{ x }7/4\text{ x }7/4\left( 14/3\text{ }+\text{ }2/3\text{ x }7/4 \right) \\ =\text{ }77/8\left( 14/3\text{ }+\text{ }7/6 \right) \\ =\text{ }77/8\left( 28+7/6 \right) \\ =\text{ }77/8\text{ }x\text{ }35/6 \\ =\text{ }2695/48 \\ =\text{ }56.15\text{ }{{m}^{3}} \\ \end{array}\]

(ii)

    \[\begin{array}{*{35}{l}} Internal\text{ }curved\text{ }surface\text{ }area\text{ }=\text{ }2\pi rh\text{ }+\text{ }2\pi {{r}^{2}}~=\text{ }2\pi r\left( h\text{ }+\text{ }r \right) \\ =\text{ }2\text{ x }22/7\text{ x }7/4\left( 14/3\text{ }+\text{ }7/4 \right) \\ =\text{ }11\left( 56\text{ }+\text{ }21 \right)/12 \\ =\text{ }11\text{ x }77/12 \\ =\text{ }847/12 \\ =\text{ }70.58\text{ }{{m}^{2}} \\ \end{array}\]

i

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