Question

Lateral surface area of a cube is 324 cm sq find its volume and tsa

Answer 1

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Here is your answer.


Lateral Surface Area of Cube is 324 sq.cm

Let the side of the Cube is x cm

As we know the formula
Lateral Surface Area of Cube= 4 × (side)^2
$324 = 4 \times {x}^{2} \\ \\ {x}^{2} = \frac{324}{4} \\ \\ {x}^{2} = 81 \\ \\ x = \sqrt{81} \\ \\ x = 9 \: cm$
Side of Cube = 9 cm
Now
As we know the formula
Volume of Cube = Side^3
$= (9) {}^{3} \\ \\ = 729 \: cm {}^{3}$
Total Surface Area of Cube = 6 × side^2
$= 6 \times 9 {}^{2} \\ \\ = 486 \: cm {}^{2}$

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Answer 2

Step-by-step explanation:

Given:

• Lateral surface area of cube is 324 cm².

To Find:

• What is its volume and total surface area?

Solution: Let the each side of cube be a cm. Then the lateral surface area of the cube = (4a²) cm².

∴ 4a² = 324

$→ {a}^{2} = \frac{324}{4} \\ \\ → {a}^{2} = 81 \\ \\ →a = \sqrt{81} \\ \\ →a = 9 \: cm$

Hence, Measure of each side of cube is of 9 cm.

★ Volume of cube = a³ cm³ ★

$→(9) ^{3} \\ \\ →(9 \times 9 \times 9) \: cm ^{3} \\ \\ →729 \: cm ^{3}$

★ TSA of cube = (6a²) sq units ★

$→ 6 \times (9) ^{2} \: cm ^{2} \\ \\ →6 \times 81 \: cm ^{2} \\ \\ →486 \: cm^{2}$