Answer:
Radius = 8 mm
Slant Height = 14 mm
Step-by-step explanation:
Base of a cone is a circle.
Area of circle is given as [tex]A=\pi r^{2}[/tex]
Where [tex]r[/tex] is the radius.
Given that
[tex]A = 64 \pi\ mm^2\\\Rightarrow \pi r^{2} = 64\pi \\\Rightarrow r^{2} = 64\\\Rightarrow r = 8\ mm[/tex]
Hence, radius is 8 mm.
Formula for Lateral Surface Area of a cone:
[tex]LSA = \pi rl[/tex]
Where [tex]r[/tex] is the radius and
[tex]l[/tex] is the slant height of cone
Given that [tex]LSA = 112 \pi\ mm^2[/tex]
[tex]\Rightarrow 112\pi = \pi \times 8 \times l\\\Rightarrow 8 \times l = 112\\\Rightarrow l = 14\ mm[/tex]
Hence, slant height is 14 mm
