Question

Cone A is similar to Cone B with a scale factor of 4:5. If thesurface area of Cone B is 860 ft^2, find the surface area of Cone A.

Answer 1

The surface area of cone A is;

`A_A=550.4\text{ }ft^2`

Step-by-step explanation:

Given that the scale factor of cone A to cone B is;

`\begin{gathered} 4\colon5 \\ =(4)/(5) \end{gathered}`

If the surface area of cone B is 860 ft^2;

`A_B=860ft^2`

The since they are similar, the surface area of the two cones can be related using the formula;

`\begin{gathered} (4)/(5)=\sqrt[]{(A_A)/(A_B)} \\ ((4)/(5))^2=(A_A)/(A_B) \\ (A_A)/(A_B)=(16)/(25) \\ A_A=(16)/(25)A_B \\ A_A=(16)/(25)(860) \\ A_A=550.4\text{ }ft^2 \end{gathered}`

Therefore, the surface area of cone A is;

`A_A=550.4\text{ }ft^2`