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3 years ago

The volume of a cube is 125m3 if I L of a paint covers 6m2, how many liters of paint are needed to paint the outside of the cube

Mathematics

1 answer:

Effectus [21]3 years ago

6 0

Answer:

36 liters

Step-by-step explanation:

step 1

Find the length side of the cube

we know that

The volume of the cube is given by

$V=b^3$

we have

$V=125\ m^3$

substitute

$125=b^3$

solve for b

$b=5\ m$

step 2

Find the surface area of the cube

The surface area of a cube is equal to

$SA=6b^2$

substitute the value of b

$SA=6(6)^2=216\ m^2$

step 3

Find out how many liters of paint are needed to paint the outside of the cube

we know that

1 L of a paint covers 6m2

so using proportion

$\frac{1}{6}\ \frac{L}{m^2} =\frac{x}{216}\ \frac{L}{m^2} \\\\x=216/6\\\\x=36\ L$

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Minchanka [31]

Answer:

156 in squared

Step-by-step explanation:

So the formulas will be stated below

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3 years ago

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4 years ago

1. A movie theater designs two bags to hold 96 cubic inches of popcorn. a. Find the height of each bag b. Which bag should the t

MrRissso [65]

I have attached a screenshot with the images of the two popcorn bags used by the theater.

Part (a):
Bag A:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 3 in
width = 4 in
Therefore:
96 = 3 * 4 * height
96 = 12 * height
height of bag A = 8 in
Bag B:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 4 in
width = 4 in
Therefore:
96 = 4 * 4 * height
96 = 16 * height
height of bag B = 6 in

Part (b):
To determine the amount of paper needed, we will need to calculate the surface of each bag. Excluding the top base, each bag will have 5 faces. Four side faces (each two opposite are equal) and the base.
Bag A:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (3*4) + 2(8*4) + 2(8*3)
Surface area = 12 + 64 + 48
Surface area of bag A = 124 in²
Bag B:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (4*4) + 2(6*4) + 2(6*4)
Surface area = 16 + 48 + 48
Surface area of bag B = 112 in²
From the above calculations, we can deduce that the theater should choose bag B in order to reduce the amount of paper needed.

Hope this helps :)