Question

Akshay took a right circular cylinder having base diameter 12cm and height 15cm and filled it completely with ice-cream. He then went to a slum area and distributed the ice-cream filled in cones of height 12cm and diameter 6cm each having a hemispherical shape on the top to the needy children. Find the number of children who will get ice cream in these cones?

Answer 1

15 children will get the ice cream

Answer 2

Answer:

Number of childrens who will get ice cream in the cones are 10 .

Step-by-step explanation:

Formula

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

$Volume\ of\ a\ cone = \pi r^{2} \frac{h}{3}$

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

Where r is the radius and h is the height .

As given

Akshay took a right circular cylinder having base diameter 12cm and height 15cm and filled it completely with ice-cream.

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

$Radius=\frac{12}{2}$

                 = 6 cm

$\pi = 3.14$

$Volume\ of\ a\ cylinder\ filled\ with\ ice\ cream = \pi r^{2} h$

                                                                                     = 3.14 × 6 × 6 × 15

                                                                                      = 1695.6 cm³

Thus

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

$Radius=\frac{6}{2}$

                 = 3 cm

$Volume\ of\ ice\ cream\ filled\ in\ cone = Volume\ of\ cone + Volume\ of\ hemisphere$

$Volume\ of\ ice\ cream\ filled\ in\ cone =3.14\times 3\times 3\times \frac{12}{3} +\frac{2}{3}\times 3.14\times 3\times 3\times 3$

$Volume\ of\ ice\ cream\ filled\ in\ cone =3.14\times 3\times 3\times 4+2\times 3.14\times 3\times 3$

Volume of ice cream filled in cone = 113.04 + 56.52

                                                         = 169.56

Let us assume that the number of childrens who will get ice cream be x .

Equation becomes

Volume of ice - cream filled in cylinder = n × Volume of ice - cream filled in cone

1695.6 = n × 169.56

$\frac{1695.6}{169.56} = n$

n = 10

Therefore the number of childrens who will get ice cream in the cones are 10 .