Aina builds a cube model out of manila cards. If the volume of the constructed cube is (2+3p) ³ cm³, find the total surface area of the cube in terms of p. HEL

Given:

The volume of a cube =

To find:

The total surface area of the cube in terms of p.

Solution:

Volume of a cube is:

           ...(i)

Where, a is the side length.

It is given that,

        ...(ii)

On comparing (i) and (ii), we get

Now, the total surface area of a cube is:

Where, a is the side length.

Putting , we get

Therefore, the total surface area of the cube in terms of p is .

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°