Question

Does anyone know the surface area for this problem. if so i will mark brainliest.

Answer 1

From the given volume, we know that the ratio is:
$\text {Ratio of yellow eraser to white eraser = } \sqrt[3]{ \dfrac{16}{2} }$

From the given area, we know that the ratio is:
$\text {Ratio of yellow eraser to white eraser = } \sqrt{ \dfrac{52}{x} }$

Equate the two ratio and solve for x:
$\sqrt[3]{ \dfrac{16}{2} } = \sqrt{ \dfrac{52}{x} }$

Cube both sides:
$\dfrac{16}{2} = \bigg(\sqrt{ \dfrac{52}{x} }\bigg)^3$

Square both sides:
$\bigg(\dfrac{16}{2} \bigg)^2 = \bigg( \dfrac{52}{x} }\bigg)^3$

Simplify each term:
$\dfrac{16^2}{2^2} = \dfrac{52^3}{x^3}$

Cross multiply:
$256x^3 = 562432$

Divide both sides by 256:
$x^3 = 2197$

Cube root both sides:
$x = 13$