Question

Ice Cream is to be filed into a cone of height 12 cm and diameter 6cm having the hemispherical space on the top in the volume of ice cream that can be filed into it.

Answer 1

Answer:

volume if conical part = 1/3 πr^2 h

= 1/3 π 9 x 12

= 36 π cm^3

volume of hemispherical part = 2/3 π r^3

= 2/3 π 27

= 18 π cm^3

total volume = 36 π + 18 π

=54 x 3.14

= 169.56cm^3

Answer 2

height $\rm (h_{1})$ of cylindrical container = 15cm

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

Radius $\rm (r_{1})$ of circular end of container = 12/2 = 6cm

Radius $\rm (r_{2})$ of circular end of ice cream cone = 6/2 = 3cm

Height $\rm (h_{2})$ of conical part of ice- cream cone = 12cm

Let ice-cream cones be filled with Ice-cream of the container.

volume of Ice-cream in cylinder = n (volume of 1 Ice-cream cone + volume of Hemi spherical shape on the top)

$\rm\implies\pi {r}^{2} h = h( \frac{1}{3} \pi {r}^{2} 3h2 + \frac{2}{3} \pi {r}^{3} 2)$

$\rm\implies\pi \times {6}^{2} \times 15 = n( \frac{1}{3} \pi {3}^{2} \times 12 + \frac{2}{3} \pi {3}^{3} )$

$\rm\implies n = \frac{30 \times 15}{ \frac{1}{3} \times 9 \times 12 + \frac{2}{3} \times 27}$

$\rm\implies n = \frac{36 \times 15 \times 3}{108 + 54}$

$\rm\implies n = 10$

So, 10 Ice-cream cones can be filled with Ice-cream in the Container.