Question

2. If the lateral surface area of a cube is given as 64 sq. cm, find the total surface area of the cube.

3. Find the length of the longest diagonal of a cube of edge 9 cm.​

Answer 1

Answer:

2. 96 sq. cm

3. 9√3 cm

Step-by-step explanation:

2. Let the side of the cube be a

We know, lateral surface area of cube = 4a^2

According to the problem:

4a^2 = 64

or, a^2 = 64/4

or, a^2 = 16

or, a = ±√16

or, a = ±4

Since length can't be less than 0, we eliminate -4.

Thus, a = 4

We know, total surface area of a cube = 6a^2

Putting value of a,

6×4×4 cm= 96 sq. cm

3. Side of cube = 9 cm

We know, diagonal of a cube =√3 × side

Putting the value,

√3 ×9 cm = 9√3 cm