Question

A container shaped like a right circular cylinder having 6cm radius and height 15cm is full of ice cream. It is distributed equally to 10 student's in cone shaped cups. If the height of the cone is 6 times the radius, find the radius and height of cone.​

Answer 1

cylinderical shaped container with ice-cream have

radius, r = 6 cm

height, h = 15 cm

$volume \: of \: cylinder \: = \pi {r}^{2}h \\ \\ volume \: of \: container \: = \pi \: {6}^{2} \times 15 \\ \\ volume \: of \: container \: = 540 \: \pi \: \: {cm}^{3}$

NOW,

as given that

ice-cream is distributed to 10 students equally in cobe shaped cups

It is also given that height of the cones is 6 times the radius of cones

so, let radius of be x then, height will be 6x

And volume of 10 cones will be equal to the volume of cylindrical container

So,

volume of container = 10 × (volume of cone)

$(as</u></em></strong><strong><em><u>,</u></em></strong><strong><em><u> </u></em></strong><strong><em><u>\: volume \: of \: cone \: = \frac{1}{3} \pi \: {(radius)}^{2} (height))$

Hence,

$540 \: \pi = 10( \frac{1}{3}\pi \: {x}^{2} (6x)) \\ \\ \frac{540\pi}{10} = \frac{1}{3}\pi {x}^{2} (6x) \\ \\ 54\pi = \frac{6\pi {x}^{3} }{3} \\ \\ (\pi \: will \: be \: eliminated \: being \: on \: both \: sides) \\ 54 = 2 {x}^{3} \\ \\ {x}^{3} = 27 \\ \\ x = \ \sqrt[3]{27} \\ \\ x = 3 \: cm$

HENCE,

RADIUS OF CONE WILL BE 3 CM

AND

HEIGHT OF CONE = 6x = 6 (3) = 18 CM.

Answer 2

Height = h = 12.48 cm

Radius = r = 2.08 cm