Question

The surface area of cube is 1350 cm2find the volume of the cube​

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• TSA of a cube = 1350 cm².

${\underline{\underline{\bf{To\:find:}}}}$

• The volume of the cube.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{TSA}_{[Cube]}=6a^2\:sq.units}}}$

$\underline{\boxed{\sf{{Volume}_{[Cube]}=a^3\:cu.units}}}$

$\:\:\:\:\:\:\:\:\:\sf{\bullet\:a=side}$

${\underline{\underline{\bf{Solution:}}}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎We're only given with the measure of TSA of the cube. We've to find the volume of the cube. So, first we shall find the measure of side of the cube and then it's volume.

Side of the cube:

As we know the TSA, we can find it by substituting the given measure in the formula:

$\rightarrowtail{\sf{TSA=6a^2\:sq.units}}$

The value of $\sf{\pi}$ can be taken as $\sf{\frac{22}{7}}$.

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{1350=6a^2}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{\dfrac{1350}{6}=a^2}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{225=a^2}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{\sqrt{225}=a}}$

$\:\:\:\:\:\:\:\:\:\mapsto\underline{\sf{15\:cm=a}}$

$\red\bigstar$ Volume of the cube:

Now, by inserting the obtained measure of side in the formula:

$\rightarrowtail{\sf{a^3\:cu.units}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{15^3}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{15\times 15\times 15}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{225\times 15}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\frak{\red{\underline{\underline{3,375\:{cm}^{3}}}}}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• The volume of the cube which has surface area of 1,350 cm² is 3,375 cm³.

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