Question

Find the Volume of a cube if its total surface area is 150 cm square.

Answer 1

Given :

• The Total Surface Area of a cube = 150 cm²

To Find :

• The Volume of Cube.

Solution :

• First, we need to find one Side of the cube.

We know that : TSA of a Cube = 6a²

$\longrightarrow$ 150 = 6a²

$\longrightarrow$ a² = 150/6

$\longrightarrow$ a² = 25

$\longrightarrow$ a = √25

$\longrightarrow$ a = 5

• Hence, the side of the Cube = 5 cm.

• Finding Volume of the Cube.

Using Formula : Volume of a Cube = a³

$\longrightarrow$ Volume of a cube = 5³

$\longrightarrow$ Volume of a cube = 5 × 5 × 5

$\longrightarrow$ Volume of a cube = 125 cm³

• Hence the Volume of the Cube = 125 cm³.

Answer 2

Given :-

• Total surface area of cube = 150 cm².

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To find :-

Volume of cube?

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Solution :-

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☯ Let sides of cube be x cm.

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We know that,

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$\sf\;{\boxed{\sf{\purple{Total\;surface\;area_{\;(cube)} = 6a^2}}}}$

$:\implies\sf 6 \times x^2 = 150$

$:\implies\sf x^2 = \cancel{ \dfrac{150}{6}}$

$:\implies\sf x^2 = 25$

$:\implies\sf \sqrt{x^2} = \sqrt{25}$

$:\implies{\boxed{\sf{\pink{x = 5\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Side\;of\;cube\;is\; \bf{5\;cm}.}}}$

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Now, Finding Volume of cube,

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$\sf\;{\boxed{\sf{\purple{Volume_{\;(cube)} = (side)^3}}}}$

$\qquad:\implies\sf (5)^3$

$\quad\::\implies{\boxed{\sf{\pink{125\;cm^3}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Side\;of\;cube\;is\; \bf{125\;cm^3}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}$

• Curved surface area of cube = 4a²

• Curved surface area of cuboid = 2(l + b)h

• Total surface area of cuboid = 2(lb + bh + hl)

• Volume of cuboid = l × b × h