Question

Select the correct answer from each drop-down menu. figure A: (in pic) figure B: (in pic) figure C: (in pic) figure D: (in pic) figure E: (in pic) Among these figures, figure __ and figure __ have the same volume.

Answer 1

Answer:

Figures C and D have the same volume

Step-by-step explanation:

Part 1) Find the volume of Figure A

we know that

The volume of a cone is equal to

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

where

B is the area of the base

h is the height of the cone

In this problem we have

$B=20\ cm^{2}$

$h=5\ cm$

substitute

$V=\frac{1}{3}(20)(5)=33.33\ cm^{3}$

Part 2) Find the volume of Figure B

we know that

The volume of a cylinder is equal to

$V=Bh$

where

B is the area of the base

h is the height of the cylinder

In this problem we have

$B=20\ cm^{2}$

$h=6\ cm$

substitute

$V=(20)(6)=120\ cm^{3}$

Part 3) Find the volume of Figure C

we know that

The volume of a cylinder is equal to

$V=Bh$

where

B is the area of the base

h is the height of the cylinder

In this problem we have

$B=20\ cm^{2}$

$h=5\ cm$

substitute

$V=(20)(5)=100\ cm^{3}$

Part 4) Find the volume of Figure D

we know that

The volume of a rectangular prism is equal to

$V=Bh$

where

B is the area of the base

h is the height of the prism

In this problem we have

$B=20\ cm^{2}$

$h=5\ cm$

substitute

$V=(20)(5)=100\ cm^{3}$

Part 5) Find the volume of Figure E

we know that

The volume of a pyramid is equal to

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

where

B is the area of the base

h is the height of the pyramid

In this problem we have

$B=20\ cm^{2}$

$h=10\ cm$

substitute

$V=\frac{1}{3}(20)(10)=66.66\ cm^{3}$

Answer 2

Answer:

Among these figures, figure C and figure D have the same value

Step-by-step explanation: