Question

conical cap is moulded on one end of cylinder total height of vessel is 11cm and radius is 3cm slant height of cap is 5cm find its volume​

Answer 1

Step-by-step explanation:

Let the height of the conical cap be 'h'.

Slant height (l) = 5cm.

Radius (r) = 3cm

By Pythagoras' Theorem,

$( {5cm}^{2} ) = ( {hcm}^{2} ) + (3 {cm}^{2} ) \\ = > ( {hcm}^{2} ) = ( {5cm}^{2}) - ( {3cm}^{2} ) \\ = > ( {hcm}^{2} ) = 25 {cm}^{2} - 9 {cm}^{2} \\ = > 16 {cm}^{2} \\ hcm = \sqrt{16 {cm}^{2} } = 4cm$

Therefore,h = 4cm

Height of Cylinder = (11cm - 4cm) = 7cm

Therefore, Volume of Cylinder

$\pi {r}^{2} h \\ = \frac{22}{7} \times 3cm \times 3cm \times 7cm \\ = 22 \times 3cm \times 3cm \times 1cm \\ = 198 {cm}^{3}$

Volume of cone

$\frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \times \frac{22}{7} \times 3cm \times 3cm \times 4cm \\ = 1 \times \frac{22}{7} \times 1cm \times 3cm \times 4cm \\ = \frac{264}{7} {cm}^{3} \\ = 37.71 {cm}^{3}$

Total Volume = 198.00cm³ + 37.71cm³ = 235.71cm³

Hence, Volume of the full vessel = 235.71cm³

HOPE THIS HELPS YOU.