Question

In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, the quantity of juice which a person will get is
(a) 135 πcm³ (b) 117 πcm³ (c) 99 πcm³ (d) 36 πcm³

Answer 1

The quantity of juice which a person will get is (b) 117π cm³.

The image given in the question is attached below.

Step-by-step explanation:

From diagram, we can understand that there is a inverted hemisphere in the bottom and the container is in cylindrical shape.

We need to find quantity of juice we can fill in the glass container. Since, the hemisphere is inverted then we need to neglect the volume of the hemisphere from the volume of cylinder.

Quantity of juice in cylinder = Volume of cylinder - Volume of hemisphere

Let 'h' be height of the cylinder = 15 cm

Let 'r' be radius of the cylinder = 3 cm

Volume of cylinder:

$\bold{V_1=(\pi) r^{2} h}$

Volume of hemisphere:

$\bold{V_2=\frac{2}{3}(\pi) r^{3}}$

Quantity of juice in cylinder:

$\bold{V=V_1-V_2}$

$\bold{V=(\pi) r^{2} h-\frac{2}{3} (\pi) r^{3}}$

On substituting the values of height and radius, we get,

$\bold{V=[(\pi) \times 9 \times 15]-\frac{2}{3} \times(\pi) \times 3^{3}}$

$\bold{V=(\pi) \times[135-18]}$

$\bold{\therefore V=117(\pi) \ cm^3}$