Question

A vessel is the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5. Find its capacity. (Give ans with steps)

Answer 1

height of hemi= 14.5cm
radius of hemi=10.5cm
height of cylinder=14.5-10.5=4cm
capacity=volume of hemi + volume of cylinder
=2/3#r^3+#r^2h ......#=pie
=#r^2 (2/3*r+h)
=10.5^2 (2/3*10.5+4)
=110.25*11
=1212.75cm^3

Answer 2

Answer:

Total capacity of the vessel is  3808.035 cm³ .

Step-by-step explanation:

Formula

$Volume \ of\ a\ hemispherical\ bowl = \frac{2}{3}\pi r^{3}$

$Volume\ of\ a\ cylinder = \pi r^{2}\ h$

Where  r is the radius and h is the height .

As given

A vessel is the form of a hemispherical bowl surmounted by a hollow cylinder.

The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5.

$Radius = \frac{Diameter}{2}$

$Radius = \frac{21}{2}$

Radius = 10.5 cm

Height of the cylinder = Height of the vessel - Radius of the hemisphere .

                                     = 14.5 - 10.5

                                     = 4 cm

$\pi = 3.14$

Put all the values in the formula

$Total\ capacity\ of\ vessel = \frac{2}{3}\times 3.14\times 10.5\times 10.5\times 10.5 + 3.14\times 10.5\times 10.5\times 4$

$Total\ capacity\ of\ vessel = \frac{2\times 3624.9425}{3}+ 1384.74$

$Total\ capacity\ of\ vessel = \frac{7269.885}{3}+ 1384.74$

$Total\ capacity\ of\ vessel = 2423.295+ 1384.74$

Total capacity of vessel = 3808.035 cm³

Therefore the total capacity of the vessel is  3808.035 cm³ .