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castortr0y [4]
2 years ago
7

Find the volume of a cube whose surface area is 150 ft2?

Mathematics
2 answers:
s344n2d4d5 [400]2 years ago
8 0

Hey ! there

Answer:

  • Volume of cube is <u>1</u><u>2</u><u>5</u><u> </u><u>ft³</u><u> </u><u>.</u>

Step-by-step explanation:

In this question we are given with <u>surface </u><u>area </u><u>of </u><u>cube </u><u>that </u><u>is </u><u>1</u><u>5</u><u>0</u><u> </u><u>ft²</u><u> </u><u>.</u> And we're asked to find the <u>volume</u><u> of</u><u> cube</u><u> </u><u>.</u>

For finding volume of cube, we need to find the edge of the cube and formula for finding surface area of cube i.e. ,

\quad \quad   \underline{\boxed{\frak{Surface \:  Area_{(Cube)}  = 6(edge) {}^{2} }}}

<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>

As in the question it is given that surface area of cube is 150 . So ,

\quad \: \hookrightarrow \qquad \:  \sf{150 = 6(edge) {}^{2} }

Dividing with 6 on both sides :

\quad \: \hookrightarrow \qquad \:  \sf{  \cancel{\dfrac{150}{6} } =  \dfrac{ \cancel{6}(edge) {}^{2}}{ \cancel{6} } }

Simplifying it ,

\quad \: \hookrightarrow \qquad \:  \sf{ (edge) {}^{2}  = 25}

Now for removing square , taking square root to both sides :

\quad \: \hookrightarrow \qquad \:  \sf{   \sqrt{(edge) {}^{2} }  =  \sqrt{25}}

We get ,

\quad \: \hookrightarrow \qquad \:    \underline{\boxed{\sf{ edge = 5 \: ft}}}

  • <u>Therefore</u><u> </u><u>,</u><u> </u><u>edge </u><u>of </u><u>cube </u><u>is </u><u>5</u><u> </u><u>ft </u><u>.</u>

As we know the edge of cube , so we can easily find the volume of cube . We know that ,

\quad \qquad \:    \underline{\boxed{\frak{Volume_{(Cube)} = (edge) {}^{3} }}}

Now ,

\quad \longmapsto \qquad \: (5) {}^{3}

We get ,

\quad \longmapsto \qquad \:    \green{\underline{\boxed{\frak{125 \: ft {}^{3} }}}} \quad \bigstar

  • <u>Henceforth</u><u> </u><u>,</u><u> </u><u>volume</u><u> of</u><u> cube</u><u> is</u><u> </u><u>1</u><u>2</u><u>5</u><u> </u><u>ft³</u><u> </u><u>.</u>

<h2><u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>
Brrunno [24]2 years ago
7 0

Given:

  • Surface area of cube = 150 ft²

To Find:

  • Volume of cube

Solution:

As here in Question we are given Surface area of cube is 150 sq. feet. So, firstly we have find the side of edge of cube. Let 'a' be the edge of the cube

We know that,

\: \: \: \: \dashrightarrow \sf \: \: \: \: Surface  \: area_{(Cube)} = 6a^2  \\  \\

Substituting the required values,

\: \: \: \: \dashrightarrow \sf \: \: \: \: 150 = 6a^2  \\  \\ \: \: \: \: \dashrightarrow \sf \: \: \: \:   \frac{150}{6}   =  {a}^{2}  \\  \\ \: \: \: \: \dashrightarrow \sf \: \: \: \: 25 =  {a}^{2}  \\  \\ \: \: \: \: \dashrightarrow \sf \: \: \: \:  \sqrt{25}  = a \\  \\ \: \: \: \: \dashrightarrow \sf \: \: \: \: { \underline{ \boxed{ \sf{ \pink{5 = a}}}} } \\  \\

  • Edge of the cube is 5 feet

Now,

\: \: \: \: \dashrightarrow \sf \: \: \: \: Volume = (edge)^3 \\  \\ \: \: \: \: \dashrightarrow \sf \: \: \: \: Volume = (5)^3 \\  \\ \: \: \: \:\dashrightarrow \sf \: \: \: \: {\underline{\boxed{\sf{\pink{Volume =125 \: {ft}^{3}}}}}}  \\  \\

Hence,

  • Volume of the cube is 125 cu. feet
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Answer:

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How can I solve this problem
jolli1 [7]

Answer:

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Step-by-step explanation:

I'm going to use letters to label the parts of the triangle while explaining how to solve for x:

Angle A = x (bottom left angle of the triangle)

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A line has a angle measurement of 180 degrees.

Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.

To find Angle C, we would subtract Angle D's equation from 180 like this:

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Now we have all the angles inside the triangle. To find x, we are going to sum up  Angle A, B, & C and set it equal to 180.

We set the equation to 180 because a the sum of the interior angles for a triangle is 180.

The equation looks like this:

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Now we use basic algebra to solve it:

(180 - (3x + 54)) + 4x + x = 180

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(add like terms on the left side of the equation)

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To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.

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Answer:

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Answer:

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e-lub [12.9K]
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<em><u>Solution:</u></em>

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The figure is attached below

In a right triangle, the sine of the angle is the ratio of the side opposite to the angle to the hypotenuse

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