Question

the surface area of the cube is 294cm²

find it's volume

please give the right answer​​

Answer 1

Answer:

• 343 cm³ is the required volume of cube.

Step-by-step explanation:

According to the Question

It is given that,

• Surface area of Cube = 294 cm²

we have to calculate the volume of Cube .

As we know Surface Area of Cube is calculated by

• Surface Area of Cube = 6×Side²

substituting the value we get

⇢ 6 × Side² = 294

⇢ Side² = 294/6

⇢ Side² = 49

⇢ Side = √49

⇢ Side = 7 cm

Now, calculating its volume

• Volume of Cube = Side³

substituting the value we get

⇢ Volume of Cube = 7 × 7 × 7

⇢ Volume of Cube = 343cm³

• Hence, the volume of cube is 343 cm³.

Additional Information !!

$\begin{gathered}\boxed{\begin {array}{cc}\\ \quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}$

Answer 2

Answer:

Given :-

• The surface area of the cube is 294 cm².

To Find :-

• What is the volume of a cube.

Formula Used :-

$\clubsuit$ Total Surface Area Of Cube Formula :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Total\: Surface\: Area_{(Cube)} =\: 6 \times (Side)^2}}}\: \: \: \bigstar$

$\clubsuit$ Volume Of Cube Formula :

$\bigstar\: \: \sf\boxed{\bold{\pink{Volume_{(Cube)} =\: (Side)^3}}}\: \: \: \bigstar$

Solution :-

First, we have to find the side of the cube :

Given :

• Surface area of the cube = 294 cm²

According to the question by using the formula we get,

$\small \implies \bf Total\: Surface\: Area_{(Cube)} =\: 6 \times (Side)^2$

$\implies \sf 294 =\: 6 \times (Side)^2$

$\implies \sf \dfrac{\cancel{294}}{\cancel{6}} =\: (Side)^2$

$\implies \sf \dfrac{49}{1} =\: (Side)^2$

$\implies \sf 49 =\: (Side)^2$

$\implies \sf \sqrt{49} =\: Side$

$\implies \sf \sqrt{\underline{7 \times 7}} =\: Side$

$\implies \sf 7 =\: Side$

$\implies \sf\bold{\blue{Side =\: 7}}$

Hence, the side of the cube is 7 cm .

Now, we have to find the attached volume of the cube :

Given :

• Side = 7 cm

According to the question by using the formula we get,

$\dashrightarrow \bf Volume_{(Cube)} =\: (Side)^3$

$\dashrightarrow \sf Volume_{(Cube)} =\: (7)^3$

$\dashrightarrow \sf Volume_{(Cube)} =\: (7 \times 7 \times 7)$

$\dashrightarrow \sf Volume_{(Cube)} =\: (49 \times 7)$

$\dashrightarrow \sf\bold{\red{Volume_{(Cube)} =\: 343\: cm^3}}$

$\sf\bold{\purple{\underline{\therefore\: The\: volume\: of\: the\: cube\: is\: 343\: cm^3\: .}}}$

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