Question

What is the volume and surface area of this cone?

Answer 1

Volume = 261.8 cm³

Surface area = 254.2 cm²

Explanation:

To calculate the volume of the cone, we have to use the following formula:

`\boxed{V = (1)/(3) \pi r^2 h}`,

where:

V ⇒ volume

r ⇒ radius = 5 cm

h ⇒ height = 10 cm

Using the above formula and the provided measures, we get:

V =
`(1)/(3)` × π × (5)² × 10

=
`(1)/(3)` × π × 25 × 10

= 261.8 cm³

In order to calculate the surface area of the cone, we have to use the following formula:

`\boxed{SA = \pi r^2 + \pi r l}`

where:

SA ⇒ surface area

r ⇒ radius = 5 cm

l ⇒ slant length =
`√(r^2+h^2)` =
`√(5^2+10^2)` = 5√5 cm

Using the formula,

SA = π × (5)² + π × 5 × 5√5

= π × 25 + π × 25√5

= 254.2 cm²