Question

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

Answer 1

Hey ! there

Answer:

• Volume of cube is 125 ft³ .

Explanation:

In this question we are given with surface area of cube that is 150 ft² . And we're asked to find the volume of cube .

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) }}}`

Solution : -

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{(150)/(6) } = \frac{ \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) } = √(25)}`

We get ,

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

• Therefore , edge of cube is 5 ft .

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`

• Henceforth , volume of cube is 125 ft³ .

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Answer 2

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 \: \: \: \: (150)/(6) = {a}^(2) \\ \\ \: \: \: \: \dashrightarrow \sf \: \: \: \: 25 = {a}^(2) \\ \\ \: \: \: \: \dashrightarrow \sf \: \: \: \: √(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