Question

The cross-sectional areas of a right pyramid and a right cylinder are congruent. The right pyramid has a height of 10 units, and the right cylinder has a height of 7 units. Which conclusion can be made from the given information?

Answer 1

Answer:

The volume of the cylinder is 2.1 times the volume of the pyramid

Step-by-step explanation:

step 1

Find the volume of the pyramid

we know that

The volume of a right pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the base of pyramid

H is the height of the pyramid

we have

$H=10\ units$

substitute

$Vp=\frac{10}{3}B\ units^{3}$

step 2

Find the volume of the right cylinder

we know that

The volume of right cylinder is equal to

$V=BH$

where

B is the area of the base of cylinder

H is the height of the cylinder

we have

$H=7\ units$

substitute

$Vc=7B\ units^{3}$

step 3

Compare the volumes

we know that

The area of the base both figures are congruent

Find the ratio of their volumes

$\frac{Vp}{Vc}$

substitute

$\frac{Vp}{Vc}=\frac{(\frac{10}{3}B)}{7B}$

Simplify

$\frac{Vp}{Vc}=\frac{10}{21}$

$21Vp=10Vc\\\\Vc=2.1Vp$

therefore

The volume of the cylinder is 2.1 times the volume of the pyramid

Answer 2

Answer:

Volume of right cylinder =2.1 times the volume of right pyramid

Step-by-step explanation:

We are given that Cross-sectional area of right pyramid and a right cylinder are congruent.

The height of pyramid =10 units

The height of right  cylinder =7 units

We have to find the conclusion that can be made from given information.

We know that Volume of right cylinder =$\pi r^2h$

Volume of right pyramid =$\frac{1}{3}Bh$

Where B=Area of base of pyramid

Volume of right  cylinder =$\pi r^2{7}=7\pi r^2$

We know that base area of right cylinder=B =$\pi r^2$

Therefore, volume of cylinder =$7B$

Volume of right pyramid =$\frac{1}{3}\times 10\times B$

Volume of right pyramid =$\frac{10}{3} B$

We are given that cross section area  of right pyramid is congruent to  cross section area of right cylinder

$\frac{volume\;of\;\;right\;cylinder}{volume\;of\;right\;pyramid}=$$\frac{7B}{\frac{10}{3}B}$

$\frac{volume\;of\;right\;cylinder}{volume\;of\;right\;pyramid}$=$\frac{21}{10}$=2.1

Volume of right cylinder =2.1 times the volume of right pyramid

Therefore, the conclusion is volume of cylinder is 2.1 times the volume of pyramid .