Question

4. A right cone has a surface area of 258 cm² and a base radius of 4 cm. What is

the height of the cone to the nearest tenth of a centimetre?

Answer 1

h = 16.0 cm

Explanation:

Note: I am assuming that the surface area of 258 is the total surface area which includes the Lateral Area (L) and Base Area(B)

Total Surface Area of a right cone

= Lateral Area(L) + Base Area(B)

All numbers in intermediate calculations are rounded to tenth of centimeter i.e. 1 decimal point

Base Area is the area of the circle with radius 4 =
`\displaystyle \pi \cdot16 = 50.3` cm²
Total Area = 258 cm²

So Lateral Area = 258 - 50.3 = 207.7 cm²

Lateral Area is given by the formula

`\displaystyle L = \pi r s \textrm{ where s is the slant height }`

So we get

`\displaystyle \rm pi \cdot 4 \cdot s = 207.7\\\\\textrm {This gives } s = (207.7)/(4\pi) = 16.5\\\\` cm

Slant height is given by the formula:

`s = √(r^2 + h^2) \textrm{ where r is the radius and h the height}`
Plugging in values we get

`16.5 = √(4^2 + h^2) = √(16 + h^2)`

Square both sides

`16.5^2 = 16 + h^2`

==>
`h^2 = 16.5^2 - 16 = 256.25\\\\h = √(256.25) = 16.003 = 16.0` rounded to 1 decimal place

So final answers is h = 16 cm

Answer 2

64.5cm

Explanation:

I hope this answer help you