Answer:
D. [tex]\frac{1}{3} *3.14*3^{2} *7[/tex]
Step-by-step explanation:
Given :
A cylinder having radius = 3 feet
Height = 7 feet
To Find : the volume of a cone that fits exactly inside the cylinder
Solution :
Refer the attached figure then you can observe that when the radius and height of the cone will be equal to radius and height of the cylinder only then cone fits exactly inside the cylinder
Now to check which of the following option is that volume of the cone that fits into the given cylinder .
Volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex] ---(a)
where [tex]\pi =3.14[/tex]
now r (radius) and h(height) in this formula should be equal to r and h of the given cylinder
Consider Option A : VOLUME OF CONE : [tex]3.14*7^{2} *3[/tex]
If we compare this option with the formula (a)
first this is not the volume of cone since 1/3 is missing
Then r = 7 and h = 3
while r =3 and h = 7 of given cylinder
So option A cone cannot get fits into the given cylinder .
Thus option A is wrong .
Consider Option B : VOLUME OF CONE : [tex]\frac{1}{3} *3.14*7^{2} *3[/tex]
If we compare this option with the formula (a)
Then r = 7 and h = 3
while r =3 and h = 7 of given cylinder
So option B cone cannot get fits into the given cylinder .
Thus option B is wrong .
Consider Option C : VOLUME OF CONE : [tex]3.14*3^{2} *7[/tex]
If we compare this option with the formula (a)
We will see that this is not the volume of cone since 1/3 is missing
Thus the option C is wrong
Consider Option D : VOLUME OF CONE : [tex]\frac{1}{3} *3.14*3^{2} *7[/tex]
If we compare this option with the formula (a)
formula used is correct
and r = 3 and h = 7
Since r and h of this volume of cone is equal to r and h of given cylinder . So, this cone fits into given cylinder .
Thus Option D IS CORRECT .
