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3 years ago

If each dimension of the rectangular prism is doubled, how will its total surface area change?

Mathematics

2 answers:

lilavasa [31]3 years ago

7 0

Answer:

Option C is correct.

The surface area increases by a factor of four.

Step-by-step explanation:

A rectangular prism is also known as a cuboid.

Take a rectangular prism for example with length, width and height given as x, y and z respectively.

The surface area of the rectangular prism is given as

S = 2xy + 2yz + 2xz = 2(xy + yz + xz)

If all the dimensions are now doubled, the length, width and height all become 2x, 2y and 2z respectively.

The new surface are is then

S₁ = 2(2x)(2y) + 2(2y)(2z) + 2(2x)(2z)

S₁ = 8xy + 8yz + 8xz

S₁ = 4 [2xy + 2yz + 2xz]

Showing that the new surface area = 4 × the old surface area.

S = 2xy + 2yz + 2xz

S₁ = 4 × S = 4S.

Hope this Helps!!!

BARSIC [14]3 years ago

4 0

2(wl+hl+hw) is the surface area of the rectangular prism
If you were to double the dimensions
2(2w2l+2h2l+2h2w)
This simlifies to
8(wl+hl+hw).
The surface area increases by a factor of four.

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Aaron has 5 cups of dough to make dumplings. if he uses 1/2 cup o dough for each dumpling, how many dumplings can Aaron make?

nirvana33 [79]

The number of dumpling Aaron can make is 10 dumplings

<h3>How to find the number of dumpling using cups?</h3>

Aaron has 5 cups of dough to make dumplings.

He uses 1 / 2 cup of dough for each dumpling.

Therefore, the number of dumpling Aaron can make can be calculated as follows:

1 / 2 cups of dough = 1 dumpling

5 cups of dough = ? dumpling

cross multiply

Hence,

number of dumpling = 5 ÷ 1 / 2

number of dumpling = 5 × 2

number of dumpling = 10 dumplings

Therefore, the number of dumpling Aaron can make is 10 dumplings.

learn more on cups here: brainly.com/question/14395071

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2 years ago

What is the following number in decimal form?

belka [17]

The correct answer is b

7 0

3 years ago

A brewery has a beer dispensing machine that dispenses beer into the company's 12 ounce bottles. The distribution for the amount

-Dominant- [34]

Answer:

The company should use a mean of 12.37 ounces.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.17 ounce.

This means that $\sigma = 0.17$

The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)?

This is $\mu$ , considering that when $X = 12$ , Z has a p-value of $1 - 0.985 = 0.015$ , so when $X = 12, Z = -2.17$ .