Question

What part of the volume of a cube is the pyramid whose base is the base of then cube and whose vertex is the center of the cube?
A) 4:1
B) 5:1
C) 6:1
D) 7:1

Answer 1

Hey.


Here is your answer.


We know that volume of the cube is


V = (side)^3 or

${a}^{3}$





Also the base of the cube and pyramid are same

i.e. , on the same sides (a) of the cube


Also, Volume of a pyramid =


$( \frac{1}{3} \times {a}^{2} \times \frac{a}{2} )$


So, their ratio will be


$= \: \frac{ {a}^{3} }{( \frac{1}{3} \times {a}^{2} \times \frac{a}{2} )} \\ \\ = \: \frac{{a}^{3}}{ \frac{ {a}^{3} }{6} } \\ \\ \: = \: \frac{6}{1} \: \: = 6$



So, the answer is © 6 : 1.


Thank you.

Answer 2

Heya....

==== Option C , 6:1 is correct ...

Solution :-

Volume of cube is = a^3


Volume of pyramid is = ( 1/3*a^2*a/2 )

So... the ratio will be ...

a^3/1/3*a*a/2 = a^3/a^3/6

= 6/1 = 6:1

Thank you