The cone shown has a volume of 12π in3. find the volume of a cylinder with the same base and height as the cone.
a) 4π in3
b) 9π in3
c) 24π in3
d) 36π in3

The correct option is D.

Step-by-step explanation:

The volume of cone is 12π in³.

The volume of cone is

Multiply both sides by 3.

Divide both sides by π.

                            ..... (1)

It is given that base and height of cone and cylinder are equal.

The volume of cylinder is

Using equation (1), we get

Therefore the volume of cylinder is 36π and option D is correct.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.