A company sells color sand for use in art projects. They are trying to decide which of the two cylindrical Packages shown to use.
The basis of both packages are congruent to one another. Which statement correctly compares the volumes of the two packages and explains the comparison?

package a has a greater volume because the sides of the cylinder are perpendicular to the bases

package B has a greater volume because more material is required to make the slanted sides of the cylinder

The two packages have the same volume because their bases are congruent and they have the same height

it is not possible to determine which package has a greater volume without knowing the angle at which package B is inclined

Question

juicewrld431 juicewrld431

04-05-2021
Mathematics

contestada

A company sells color sand for use in art projects. They are trying to decide which of the two cylindrical Packages shown to use.
The basis of both packages are congruent to one another. Which statement correctly compares the volumes of the two packages and explains the comparison?

package a has a greater volume because the sides of the cylinder are perpendicular to the bases

package B has a greater volume because more material is required to make the slanted sides of the cylinder

The two packages have the same volume because their bases are congruent and they have the same height

it is not possible to determine which package has a greater volume without knowing the angle at which package B is inclined

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facundo3141592 facundo3141592 · Answer 1 · 2021-05-13T02:40:19+02:00

Answer:

option B.

Step-by-step explanation:

We have two cylinders, such that both of them have the same base area.

Both have the same height, but cylinder A is straight, while cylinder B is inclined.

Now, let's suppose that we have two parallel lines, such that these lines are at a distance H (let's define H as the height).

Now draw one line that is perpendicular and that cuts these two lines, the length of the segment that lies between the two original lines is H.

Now draw another line, this one is not perpendicular to the first two lines, and it also intersects both of them. The segment that lies between the two original lines has a length larger than H.

The same happens for the cylinders because both have the same height, but one is slanted and the other doesn't, then the slanted one will be "longer", thus, the volume will be larger.

The correct option is B.