A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are $6 cm$ and $4 cm$ respectively. Find the height of water level in the cylinder.

Question

Toppr Admin · Accepted Answer

Correct option is C- - -dfrac-7-12-cm -Suppose water level rises by h cm- Then-Volume of a cylinder of radius 7 cm and height h - Volume of bowel- -Rightarrow -pi -times 7-2- -times h - -dfrac-2-5- -times -left - -dfrac-7-2- -right -3- -Rightarrow h - -dfrac-7-12-cm-

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

Correct option is C. $$ \dfrac{7}{12}\,cm $$
Suppose water level rises by h cm. Then,
Volume of a cylinder of radius 7 cm and height h = Volume of bowel

$$ \Rightarrow \pi \times 7^{2} \times h = \dfrac{2}{5} \times \left ( \dfrac{7}{2} \right )^{3} \Rightarrow h = \dfrac{7}{12}cm$$

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

Correct option is C. $$ \dfrac{7}{12}\,cm $$Suppose water level rises by h cm. Then,Volume of a cylinder of radius 7 cm and height h = Volume of bowel$$ \Rightarrow \pi \times 7^{2} \times h = \dfrac{2}{5} \times \left ( \dfrac{7}{2} \right )^{3} \Rightarrow h = \dfrac{7}{12}cm$$

Correct option is C. $$ \dfrac{7}{12}\,cm $$
Suppose water level rises by h cm. Then,
Volume of a cylinder of radius 7 cm and height h = Volume of bowel

$$ \Rightarrow \pi \times 7^{2} \times h = \dfrac{2}{5} \times \left ( \dfrac{7}{2} \right )^{3} \Rightarrow h = \dfrac{7}{12}cm$$