Question

the lateral surface area of a cube is 64cm find its total surface area​

Answer 1

Answer :

➥ The Total surface area of a cube = 94 cm²

Given :

➤ Lateral surface area of a cube = 64 cm

To Find :

➤ Total surface area of a cube = ?

Solution :

To find the total surface area of a cube first we need to the edge of the cube from lateral surface area of a cube formula.

As we know that

Lateral surface area of a cube = 4a²

⟾ 4a² = 64

⟾ a² = 64/4

⟾ a² = 16

⟾ a = √16

⟾ a = 4 cm

Now ,

As we know that

Total surface area of a cube = 6a²

⟾ 6a²

⟾ 6 × 4²

⟾ 6 × 4 × 4

⟾ 24 × 4

⟾ 96 cm²

Hence, the total surface area of a cube is 96 cm.

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Some related formulae :

⪼ Total surface area of a cube = 6a²

⪼ Lateral surface area of a cube = 4a²

⪼ Volume of a cube = a³

Answer 2

Given ,

LSA of cube = 64 cm²

We know that , the LSA of cube is given by

$\boxed{ \tt{LSA = 4 {(a)}^{2} }}$

Thus ,

64 = 4(a)²

(a)² = 16

a = √16

a = ± 4

Since , the length can't be negative

Now , the TSA of cube is given by

$\boxed{ \tt{TSA = 6 {(a)}^{2} }}$

Thus ,

TSA = 6 × 16

TSA = 96 cm³