Question

Conbined solid find total surface area​

Answer 1

Answer: 273π
`cm^(2)` or 857.655
`cm^(2)`

Explanation:

For this kind of question, we have to divide the parts of solid as it is easier to use different methods for each parts of the solid.

In this case, let's divide it to the cone part and the hemisphere.

The formula for the surface area of a sphere is:

4πr²

and for the cone, it is

πrl + πr²

However, in this case, we are only considering half of the surface area for the sphere therefore giving us:

2πr²

and excluding the base of the cone(πr²) it gives us

πrl

Therefore, the total area of the combined solid given can be represented as:

2πr² + πrl

given r = 31 - 24 = 7cm,

and l =
`\sqrt{24^(2) + 7^(2)}` = 25cm, (pythagorian theorum)

substituting, the answer will be

2π(7)² + π(7)(25)

= 273π
`cm^(2)` or 857.655
`cm^(2)`