Question

Cube B is the image of cube A after dilation by a scale factor of 55. If the surface area of cube A is 81 cmsquared
2
, find the surface area of cube B, the image.

Answer 1

To find the surface area of cube B after a dilation of cube A by a scale factor of 55, we can use the property of surface areas that states:

When a three-dimensional object is dilated by a scale factor \( k \), the surface area of the object is scaled by \( k^2 \).

1. Given the scale factor \( k = 55 \).
2. The surface area of cube A is given as \( 81 \, \text{cm}^2 \).

Now, we can calculate the surface area of cube B as follows:

\[
\text{Surface Area of Cube B} = \text{Surface Area of Cube A} \times k^2
\]

Calculating \( k^2 \):

\[
k^2 = 55^2 = 3025
\]

Now substituting the values:

\[
\text{Surface Area of Cube B} = 81 \, \text{cm}^2 \times 3025
\]

\[
\text{Surface Area of Cube B} = 245025 \, \text{cm}^2
\]

Therefore, the surface area of cube B is \( 245025 \, \text{cm}^2 \).