Question

if total surface area of a cube is 1014 cm, find the
lateral surface area and main diagonal of the cube​

Answer 1

Answer :

➥ The lateral surface area of a cube = 676 cm²

➥ The main diagonal of a cube = 13√3 cm

Given :

➤ Total surface area of a cube = 1014 cm

To Find :

➤ Lateral surface area of a cube = ?

➤ Main diagonal of a cube = ?

Solution :

To find lateral surface area of a cube and main diagonal of a cube first we need to find the edge of a cube from total surface area of cube formula. $\:$

As we know that

Total surface area of a cube = 6a²

→ 6a² = 1014

→ a² = 1014/6

→ a² = 169

→ a² = √169

→ a = 13 cm

Now ,

As we know that

Lateral surface area of a cube = 4a²

→ 4a²

→ 4 × 13²

→ 4 × 13 × 13

→ 52 × 13

→ 676 cm²

Hence, the lateral surface area of a cube is 576 cm².

As we know that

Main diagonal of a cube = √3a

→ √3a

→ √3 × 13

→ 13√3 cm

Hence, the main diagonal of a cube us 13√3 cm.

Answer 2

$\star\:\:\:\bf\large\underline\green{Given:—}$

Total surface area of the cube = 1014 cm²

$\star\:\:\:\large\underline\green{To\:find:—}$

Lateral surface area of the cube = ?

$\star\:\:\:\bf\large\underline\green{Solution:—}$

we know that,

$\boxed{\bf{\red{Total\:surface\:area\:of\:a\:cube=6a²}}}$

where, a = length of the cube

ATQ,

➝6a² = 1014

➝a² = 169

➝a = 13

But we also know that,

$\boxed{\bf{\blue{Lateral\:surface\:area\:of\:a\:cube=4a²}}}$

4a² = 4 × 13² cm²

= 4 × 169 cm²

= 676 cm²

Now,

$\boxed{\bf{\red{Diagonal\:of\:a\:cube=√3a}}}$

√3a = √3 × 13 cm

= 13√3 cm

Therefore, lateral surface area of the cube is 676 cm² and the main diagonal of the cube is 13√3 cm

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