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3 years ago

Help with this question, please!! I don't understand!!

Mathematics

2 answers:

TEA [102]3 years ago

6 0

Answer:

First option is correct i.e: The surface area is multiplied by 1/4

Step-by-step explanation:

Need to compare the surface area of right rectangular prism when the length, width and height are halved as compared to original length, width and height.

length =4,width =2,height =7

Area of right rectangular prism = 2(wl+hl+hw)

=2(2*4 + 7*4 + 7*2)

=2(8+28+14)

=2(50)

= 100 cm³

Now, if the length, width and height are halved, the surface area will be:

length= 2, width=1, height= 3.5

Area of right rectangular prism= 2(1*2 + 3.5*2 + 3.5*1)

= 2(2+7+3.5)

=2(12.5)

=25 cm³

if the length, width and height are halved the surface area is 25 cm³ while if original length, width and height are used the surface area is 100 cm³.

So, first option is correct i.e: The surface area is multiplied by 1/4.

olga2289 [7]3 years ago

5 0

Answer:

The first choice.

Step-by-step explanation:

The area is multiplied by (1/2)^2 = 1/4.

This is because lengths are one dimensional and areas are 2 dimensional.

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,

omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

Pyramid A

$s = 4$ -- base sides

$V = 36$ -- Volume

Pyramid B

$s = 6$ --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

$B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}$

$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

This gives:

$36 = \frac{1}{3} * 4\sqrt 3 * h$

Make h the subject

$h = \frac{3 * 36}{4\sqrt 3}$

$h = \frac{3 * 9}{\sqrt 3}$

$h = \frac{27}{\sqrt 3}$

To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

Since the heights of both pyramids are the same, we can make use of:

$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where

$s = 6$

So:

$B = \frac{1}{2} * 6^2 * sin(60)$

$B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}$

$B = 9\sqrt 3$

So:

$V = \frac{1}{3} * B * h$

Where

$B = 9\sqrt 3$ and $h = \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

$V = 81$

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