Given:
AB = 14
SO = 24
To find:
a) the volume
b) the area of the lateral surface
c) the total surface area
a) To find the volume of the cone, we will use the formula:
[tex]Volume\text{ of a cone = }\frac{1}{3}πr²h[/tex]r = radius
diameter = AB = 14
diameter = 2(radius)
radius = diameter/2 = 14/2
radius = 7
height = SO = 24
let π= 3.14
[tex]\begin{gathered} Volume\text{ of the cone = }\frac{1}{3}\times3.14\times7^2\times24 \\ Volume\text{ of the cone = 1230.88 unit}^3 \end{gathered}[/tex]b) To get the lateral surface, we will apply the formula:
[tex]\begin{gathered} lateral\text{ surface of the cone = \pi rl} \\ where\text{ l = }\sqrt{h^2+r^2} \end{gathered}[/tex][tex]\begin{gathered} Lateral\text{ surface of the cone = 3.14 }\times7\times\sqrt{7^2+24^2} \\ \\ Lateral\text{ surface area of the cone = 549.5 units}^2 \end{gathered}[/tex]c) The total surface area formula:
[tex]\begin{gathered} Total\text{ surface area of cone = Area of base + lateral surface area} \\ \\ Total\text{ surface area = \pi r}^2\text{ + \pi rl} \\ \\ Total\text{ surface area = \lparen3.14 }\times\text{ 7}^2)\text{ + 549.5} \end{gathered}[/tex][tex]Total\text{ surface area of cone = 703.36 unit}^2[/tex]