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vazorg [7]
4 years ago
9

A crate contains cylindrical cans of soup for shipment. Each crate is a cube with side lengths of 12in. Each soup can is 5in tal

l and has a diameter of 4in How many soup can will fit in each crate? Use 3.14 for π. Explain how you got your answer.
Mathematics
1 answer:
denpristay [2]4 years ago
5 0
The volume of the cube is base times width times height, or any of these measurements cubed, since they're all the same. 
Therefore, the volume of the cube is:
 12³ = 1728 in³
The volume of the cylinder is π*r²*h, where r is the radius and h is height
Remember that the diameter is twice the radius, so the radius is 2 in and the height is 5 in. 
Therefore, each can has a volume of π * 2² * 5 = 20π
Approximating π as 3.14....
The volume of each can is 62.8 in³
1728 ÷ 62.8 = 27.5
Rounding down, 27 cans can fit in the crate.
This is how I suspect the teach wanted you to solve, since it involves finding the volume of both shapes and using pi. However, this is not actually how many cans can fit, because it does not take into account the fact that not every inch of available space will be used. 

Here is another way to solve,taking this fact into account, that gives the more accurate answer:

Each can has a diameter of 4in, which means that they each require a square of 4 x 4 in to accommodate their base.
The base of each can requires 16 in² of space in the crate. 
The base of the cube is 12 x 12, so the area of the base is 144 in²
144 ÷ 16 = 9, so the base of the cube, or bottom of the box, can fit 9 cans, arranged 3 by 3. 

The cube has a height of 12 inches, and each can is 5 inches tall. Therefore, two of these stacks can fit in the box, for 9 x 2 = 18 cans. 
This is a much better answer, as it takes into account the fact that the cans can't occupy every inch of available space in the cube. 
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suppose the annual rate of inflation is about 4% this means that the cost of an item increases by about 4%. write and evaluate a
Mashcka [7]
Cost = (3,500) * (1.04)^years
Cost = (3,500) * (1.04)^4
<span><span><span>Cost = (3,500) * 1.16985856 </span> </span> </span>
<span><span>Cost = </span>4,094.50</span>



4 0
3 years ago
Someone help me pls!!!!!!
Pavel [41]

Answer:B

Step-by-step explanation:

3 0
3 years ago
Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn't make any payments
Mama L [17]

Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

A(t) = A(0)(1+r)^t

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

A(t) = A(0)(1+r)^t

A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\

It will reach $450 after t years, for which A(t) = 450, hence:

A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9

It will take about 2.9 years for Emma's balance to reach $450

Learn more about logarithm here

brainly.com/question/247340

#SPJ4 .

3 0
2 years ago
I need help to solve it
timama [110]
Notice that the two semicircles have a radius of 10/2=5 and that their area is simply the area of a complete circle with a radius of 5.  In the center you have a rectangle that is 10 by 8.  So the total area is:

A=pr^2+xy

A=25p+80 m^2

A≈158.53 which is:

A≈158.5 m^2 (to the nearest tenth of a m^2)
4 0
4 years ago
Read 2 more answers
Mason stands on the 5th step of a vertical ladder. The ladder has 15 steps, and the height difference between consecutive steps
MrMuchimi
Which number type?  I'd go with Whole numbers or integers, since the steps are just whole values one step after the next.

well, an appropriate domain, namely the inputs, well, He's on the 5th step, there are 15 steps, so he's really 10 steps away from the top of the ladder, and going down N being negative, he's -5 steps from the ground.

{ N | N ∈ ℤ ,  -5 ⩽ N ⩽ 10 }
5 0
3 years ago
Read 2 more answers
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