1 Answer

Beesasoh · Answer 1 · 2021-06-23T19:44:10+0000

Answer:

5cm^(3)

Explanation:

This problem bothers on the mensuration of solid shapes, cone an cylinder.

from the formula of cylinder and cone we can see that the volume of a cone is 3 times smaller than that of a cylinder

$volume=\pi r^(2) h$ ....................cylinder

$volume= (1)/(3) \pi r^(2)h$ .................cone

assuming all units in (cm)

Given data.

Volume of cylinder =
15cm^(3)

Diameter d=
2cm

Radius r =
(d)/(2)
= (2)/(2) = 1cm

Height h= ??

we know that the expression for the volume of a cylinder is

$volume=\pi r^(2) h$

we can substitute our given data to find the height h

$15= 3.142*1^(2)*h\\15= 3.142h$

divide both side by 3.142 we have

$h= (15)/(3.142)\\ h= 4.77cm$

We can now use this height
4.77cm and radius
1cm to find the equivalent volume of a cone.

the expression for the volume of a cone is

$volume= (1)/(3) \pi r^(2)h$

substituting our data into the expression we have

$volume= (3.142*1^(2*) 4.77)/(3) \\volume= (15)/(3) \\voulume = 5cm^(3) \\$