Question

the volume of a cube (in cubic cm) plus the Times the total length of its edges (in cms) is equal to twice its surface area (in sq. cm). the length of its diagonal is:​

Answer 1

Answer:

The measure of Diagonal of cube is  6√3 cm .

Step-by-step explanation:

Given as :

The statement are

( i ) The volume of cube plus three times total length of edges .

The volume of cube = s³ , where s is the side of cube .

As per statement

s³ + 3 ×12 s              ......1

Again

( ii ) The first statement equal to twice total surface area

∵ Total surface area of cube = 6 s²

Or, 2 × 6 s²               ..........2

Comparing the statement

s³ + 3 × 12 s = 2 × 6 s²              

Or, s³ + 3 × 12 s - 2 × 6 s² = 0

Or, s³ - 12 s² + 36 s = 0

Or, s (s² - 12 s + 36) = 0

Or, s = 0  , (s² - 12 s + 36) = 0

Or, (s² - 12 s + 36) = 0

Or, s² - 6 s - 6 s + 36 = 0

Or, s (s - 6) - 6 (s - 6) = 0

Or, (s - 6 ) (s - 6) = 0

So, s = 6  cm

So, The length of edge of cube = s = 6 cm

Now,

The measure of Diagonal of cube = l = s √3  cm

or, l = 6√3 cm

Hence, The measure of Diagonal of cube is  6√3 cm . Answer