Pls answer correctly and fast the cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information?
the volume of the triangular prism is half the volume of the cylinder.
the volume of the triangular prism is twice the volume of the cylinder.
the volume of the triangular prism is not equal to the volume of the cylinder.

The volume of the triangular prism is equal to the volume of the cylinder

Step-by-step explanation:

we know that

If the cross-sectional areas of a right triangular prism and a right cylinder are congruent

then

The area of the base (B) of both solids is congruent

step 1

Find the volume of the right triangular prism

The volume is equal to

where

B is the area of the triangular base

h is the height of the triangular prism

we have

substitute

step 2

Find the volume of the right cylinder

The volume is equal to

where

B is the area of the circular base

h is the height of the right cylinder

we have

substitute

step 3

Compare the volumes

therefore

The volume of the triangular prism is equal to the volume of the cylinder

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true