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3 years ago

Explain how to find surface area of a rectangular prism. Be specific and use examples.

1 answer:

4 0

As you can see in the picture above, there are six faces of a rectangular prism; two are formed with dimensions width and height, two are formed by the dimensions length and width, and two are formed by the dimensions length and height. So, if you know the length, width, and height of the rectangular prism, then the formula for the surface area is

=(2⋅ℎ⋅ℎ)+(2⋅ℎ⋅ℎℎ)+(2⋅ℎ⋅ℎℎ)

You might be interested in

Find the lateral and total surface area for the cone. If necessary, round to the nearest tenth and leave the

bija089 [108]

9514 1404 393

Answer:

262.2π cm²
392.16π cm²

Step-by-step explanation:

The lateral surface area is the product of half the circumference, and the slant height:

LA = πrh = π(11.4 cm)(23 cm) = 262.2π cm²

The total surface area adds the area of the base to that:

A = πr² +LA = π(11.4 cm)² +262.2π cm² = (129.96 +262.2)π cm²

A = 392.16π cm²

3 0

2 years ago

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.

Vikentia [17]

The relationship between Traingle XYZ and ACB is that they are similar triangles. tanX = tanA = 5 over 2 and 5 tenths, where

AC = 2 x XY
CB = 2 x YZ

<h3>What is the dilation about?</h3>

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, hence XYZ and ACB are similar triangles.

Angles Y and C are said to measure 90 degrees, and angles A and X are known to be congruent. Thus:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2 x XY

CB = 2 x YZ

Another way to solve for it is by:

Note that Dilation of the triangle ΔXYZ was by a factor of "2".

Since m∠Y = m∠C = 90º - given

ΔXYZ and ΔACB are said to be right triangles.

Since ∠X ≅ ∠A - given

Then ∠X and ∠Z are said to becomplementary angles

Since m∠Z = 90° - m∠X -- given

Then ∠A and ∠B are said to be complementary angles

Since m∠B = 90° - m∠A --- given

Then, ∠Z ≅ ∠B

Therefore ΔXYZ ∼ ΔACB are similar triangles because it has its corresponding sides to be proportional and its corresponding angles to be congruent.

Note:

sin ∠X = 5/5.59

sin ∠X = YZ/XY

YZ = 5 seen in ΔXYZ

XZ = 5.59 seen in hypotenuse of ΔXYZ

Then one need to Calculate the length of one aspect of XY:

XY = √((5.59)2 - 52)

= 2.4996

Note CB/YZ = 2

CD = 2*YZ = 2 x 5

= 10

AC/XY = 2

AC = 2* XY

= 2 x 2.4996

= 4.999

Learn more about dilation from:

brainly.com/question/27517432

#SPJ1

7 0

2 years ago

What is -9x+6y=18 in slope intercept form?

Scrat [10]

The answer to this question would be
y
=
1
6
x
+
3

8 0

3 years ago

Read 2 more answers

Find x for,<br> sin⁻¹ 4x + sin⁻¹ 3x = -<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%7D%7B2%7D" id="TexFormula1" title="\

Novay_Z [31]

<h2>Explanation:</h2><h2></h2>

Let's solve this problem graphically. Here we have the following equation:

$sin^{-1}(4x) + sin^{-1}(3x) = -\frac{\pi}{2}$

So we can rewrite this as:

$f(x)=sin^{-1}(4x) + sin^{-1}(3x) \\ \\ g(x)= -\frac{\pi}{2}$

So the solution to the equation is the x-value at which the functions f and g intersect. In other words:

$f(x)=g(x) \\ \\ sin^{-1}(4x) + sin^{-1}(3x) = -\frac{\pi}{2}$

Using graphing calculator, we get that this value occurs at:

$\boxed{x=-0.2}$

3 0

3 years ago

Can someone help me

erik [133]

Answer:

6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

(2x -12)/2 = arcsin(16/22×sin(24°))

x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

2x -12 = 0

x -6 = 0 . . . . . divide by 2

x = 6 . . . . . . . add 6

Then the range of values of x will be ...

6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

22² = AB² + AC² -2·AB·AC·cos(48°)

16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

22² = 2·AB²·(1-cos(48°))

16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

4 0

2 years ago

Read 2 more answers