Question

A cone of radius of 6cm is full of water. When 32 marbles each of which is a sphere of diameter 1cm are dropped into the cone, 1/18 of its water overflows. Find the height of the cone.

Answer 1

Answer:

Step-by-step explanation:

See the detailed explanation.

A cone of a radius of 6 cm is full of water  

R = 6 cm.

The volume of cone  =       (π$r^{2}$ h)/3

                          = (π×$6^{2}$ h)/3    =  12πh $cm^{3}$

The volume of sphere = $\frac{4}{3}$ π$r^{3}$    =   $\frac{4}{3}$ π×(1/2)³

                                  = π/6 $cm^{3}$

So volume of 32 sphere = 32× π/6 =  16/3 π $cm^{3}$

After dropping 32 sphere into cone, 1/18 of its water overflow means

Volume of 32 sphere = $\frac{1}{18}$ × volume of cone

$\frac{16}{3}$ π   =   $\frac{1}{18}$ × 12 π h                              h = 8 cm

Height of the cone = 8 cm.                                                 Ans

Answer 2

The height of the cone is 8 cm

Step-by-step explanation:

volume of water flown out = $\frac{1}{18}$ of volume of cone

given :

radius of cone =r= 6 cm

let the height of the cone be h

volume of cone = $\frac{1}{3}\pi r^2h$

= $\frac{1}{3} \times \frac{22}{7} \times 6\times 6\times h$

= $\frac{264}{7} \times h$ cm³

volume of water flown out = $\frac{1}{18}$ of volume of cone

= $\frac{1}{18}\times \frac{264 \times h }{7}$

= 2.095 h

volume of 1 marble

radius = 0.5 cm

volume of 1 marble = volume of sphere  = $\frac{4}{3}\pi r^3$

= $\frac{4}{3}\times \frac{22}{7} \times (0.5)^3$

= 0.524 cm³

total marbles = 32

number of marbles × volume of 1 marble = volume of water flown out

32× 0.524 =  2.095 × h

16.768 = 2.095 × h

h =$\frac{16.768}{2.095}$

h = 8

hence ,

The height of the cone is 8 cm

#Learn more:

An inverted cone is filled with water. When a cube is dropped into it, 1/11" of water from the cone  overflows. Find the length of the cube if radius of the cone is 18 cm and height is 7 cm.​

https://brainly.in/question/11457838