A rectangular prism planter is filled with potting soil. It has a length of 3 feet and a width of 8inches and a height of 8 inches. How much potting soil can it hold?

Question

A rectangular prism planter is filled with potting soil.  It has a length of 3 feet and a width of 8inches and a height of 8 inches.  How much potting soil can it hold?

anonymous · Answer

Where are you double integrals or area method?

anonymous · Answer

First we have to realize what the volume of an object is. For a rectangular prism, (which is essentially a rectangular box) that volume is simply Length * Width * Height (which is analogous to the area of a rectangle, only with the prism we add Height because we're in the third dimension.) So after realizing this, all we have to do is plug in numbers.

Whats tricky about this problem is they mix up units. So lets convert all the units to inches. 3ft is 36 inches. Now we can multiply.

36 x 8 x 8 = 2304 cubic inches

Always make sure to check your units given, which units your teacher wants the answer in.

anonymous · Answer

v= 36* 8 * 8 cubic inches

anonymous · Answer

Well, I had that but then questioned myself.  Thank you for the help.

anonymous · Answer

Heh, numbers never lie, answers sometimes do.

anonymous · Answer

What is the equation of the line that passes through the point at (1, 7) and is parrallel to the graph of 3x+y=4?

anonymous · Answer

I have no calculator so I can't figure this one out.

anonymous · Answer

Or can I ?....

anonymous · Answer

Well, parallel by definition means that the two lines have the same slope. A form that is more familiar is the slope-intercept form which is 

y = mx + b

Where m is the slope and b is the y intercept, so rearranging we get

y = -3x + 4

We can see our slope is -3

Now we need to form a new equation, with the same slope.

y2 = -3x2 + b2

We were given a point (1,7) lets just plug those points into x2 and y2 to solve for b.

7 = -3(1) + b2
b2 = 10

Which leads us to our general equation

y = -3x + 10

anonymous · Answer

Wow!  You're great.  Thank you.

anonymous · Answer

Okay, one more and I'm done!  If y=x to the -5th, which expression is equivalent to y to the 3rd?

anonymous · Answer

I don't understand the question. But I'll guess.

Since we know y = x^5, and we need to find y^3. We can simply cube both sides so we get y^3 = (x^5)^3, and when taking an exponent of an exponent we mutliply the powers, so we get y^3 = x^15.