MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

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.

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.