Find the volume of the given prism, round to the nearest tenth if necessary.

Question

annalee607 · Answer

attachment

kittiwitti1 · Answer

The volume of a rectangular/cuboid prism is $V_{prism}=l\times w\times h$

radar · Answer

This is a cube.
Volume is equal to the length times width times height.
V=lwh

radar · Answer

Supply the measurements provided and do the math.

mathstudent55 · Answer

@radar A cube is a rectangular prism with all edges congruent.
This is a rectangular prism, since all the edges are of different lengths.

For a cube: V = s^3, where s = the length of an edge.

For a rectangular prism: V = L * W * H

annalee607 · Answer

I am confused

kittiwitti1 · Answer

https://gyazo.com/d1c9d57da75778b462c43b9190db3816 Here's the formula in regards to your figure.

kittiwitti1 · Answer

Try looking at that first.

annalee607 · Answer

269.3

mathstudent55 · Answer

@AnnaLee607 
All you need to do to find the volume is multiply the length by the width by the depth.

mathstudent55 · Answer

You are correct. Just include the units, cm^3.

kittiwitti1 · Answer

Yeah, you got it right. $\text{Good job!}$ (:

annalee607 · Answer

What about this one

mathstudent55 · Answer

You need the volume?

annalee607 · Answer

yes

mathstudent55 · Answer

The volume of a prism is the area of the base times the height.

The previous problem was a rectangular prism, so the base was a rectangle.
The volume was the area of a rectangle (the base) times the height.

Here you have a triangular prism.
The base is a triangle. The volume is still the area of the base times the height.
The difference is that here you need to find the area of a triangle since the base is a triangle.
Find the area of the base and multiply by the height.

mathstudent55 · Answer

The base of this triangular prism is an equilateral triangle with side of 13 yd.

mathstudent55 · Answer

|dw:1462901333046:dw|

mathstudent55 · Answer

@AnnaLee607
Are you sure you are asked for the volume, not for the surface area?

radar · Answer

@mathstudent55 I stand corrected.

annalee607 · Answer

yes, it wants the volume

mathstudent55 · Answer

@radar Thanks, I appreciate your honesty.

mathstudent55 · Answer

Ok. Then you need to find the area of the base.

mathstudent55 · Answer

You have an equilateral triangle that I drew above.
The area of a triangle is:

$\large V = \dfrac{1}{2} bh$

To find the area of a triangle, we need a base and a height.

mathstudent55 · Answer

An equilateral triangle is also equiangular.
All angles are congruent and measure 60 degrees.
|dw:1462901564975:dw|

annalee607 · Answer

1/2*169=84.5

mathstudent55 · Answer

We can use the bottom side of 13 yd as the base for finding the area.
Now we need a height.

mathstudent55 · Answer

No. The height is not 13 yd.

mathstudent55 · Answer

Since we are using the bottom side as our base, we need the altitude drawn to that base.
An altitude of a triangle is a segment that goes from a vertex to the opposite side and is perpendicular to the opposite side.
|dw:1462901672321:dw|

mathstudent55 · Answer

In an equilateral triangle, an altitude bisects the opposite side and also bisects the angle of the vertex it starts at.
|dw:1462901826499:dw|

mathstudent55 · Answer

Notice that the two triangles created by the altitude h are 30-60-90 triangles.

mathstudent55 · Answer

The ratio of the sides of a 30-60-90 triangle is 

$\Large 1~:~\sqrt 3~:~ 2$

mathstudent55 · Answer

The sides are in order:

short leg : long leg : hypotenuse

mathstudent55 · Answer

The ratio above shows that the long leg is $\sqrt 3$ times the length of the short leg.

mathstudent55 · Answer

Since the short leg of the 30-60-90 triangle is 6.5 yd, the long leg is $6.5 \sqrt 3$ yd.
The long leg of the 30-60-90 triangle is the height of the equilateral triangle.
$6.5 \sqrt 3 \approx 11.258$
|dw:1462901986499:dw|