A cylinder and a cone have the same base and height. The cylinder can hold about 4,712 mc015-1.jpg of sand. Jared says that the cone can hold about 1,178 mc015-2.jpg of sand. Which explains whether Jared is correct?Jared is correct because the volume of the cone is less than the volume of the cylinder. The cone holds mc015-3.jpg less sand than the cylinder.Jared is correct because the cone and the cylinder have the same base and height so the cone holds mc015-4.jpgof sand.Jared is not correct because the cone and the cylinder have the same base and height so the cone holds mc015-5.jpg of sand.Jared is not correct because the volume of the cone cannot be found without knowing the radius of the base and the height of the cone.

The correct answer is C. So, lets go first to the equations that determine the volume of these solids. For the cylinder, that is simple; pi*r*r*h where r is the radius, h is the height and pi is the constant 3.14. For the cone, it is not easy to derive but one gets that the formula is:[tex]\frac{ \pi*r^2*h}{3}[/tex].

We notice thus that [tex]V_{cyl}=\pi*r^2*h=3V_{cone}[/tex]. That holds irrespective of their radius or height; we only need to know that the heights and radii of the two objects are the same. Now, we have thus that:
[tex]\frac{V_{Cyl}}{V_{Cone} } =1/3[/tex].

We can check if this holds for Jared's statement; 1178/4712=0.25=1/4. So, it does not hold and thus Jared's statement is incorrect.