Question

if the surface area of cube is 13254cm² the length of its diagonal​

Answer 1

Step-by-step explanation:

As given,

• The TSA of cube is 13254cm².

Since,

• TSA of cube = 6a² [where a is the length of edge of cube]

We can say that,

• ➠ 6a² = 13254cm²
• ➠ a² = (13254cm²)/6
• ➠ a² = 2209cm²
• ➠ a² = (47cm)² [2209 = 47²]

Comparing both sides,

• ➠ a = 47cm

We found,

• The length of edge of cube is 47cm.

Since,

• Diagonal of cube = √3 × a [where a is the length of edge of cube]

We can say that,

• ➠ Diagonal of cube = √3 × 47cm
• ➠ Diagonal of cube = 47√3 cm

Therefore,

• The length of diagonal of cube is 47√3cm.

Finalized Answer:

• The length of diagonal of cube is 47√3cm.