Gandalangviz
Answered

a right circular is inscribed in a right circular cone of altitude 2m and base radius of 1m.if the volume of the cylinder is equal to the volume of the small cone above the cylinder.find the volume and lateral area of the small cone

Sagot :

Noimeballeser91viz
Given: Radius of Cylinder= 1m
          Height of Cylinder=2m

Volume of Cylinder= πr²h
=π(1m)²(2m)
2πm³

Since the radius of the base is 1m we can assume that the small cone has 1m radius also.

Volume of Small Cone=1/3πr²h
2πm³=1/3π(1m)²h  (Volume of Cylinder=Volume of Small Cone)

Solving for h.
h=6m

Substituting h=6m
Volume of Small Cone=1/3π(1m)²(6m)
Volume of Small Cone=2πm³ or 6.28m³

By Pythagorean Theorem,
l²=h²+r²
l=√(6m)²+(1m)²
l=√37 m or 6.08m

AnneCviz
Please refer to the attached photo for the solution.

V = [tex] \frac{9}{32} [/tex] π m³

LAsmallcone = [tex] \frac{9 \sqrt{5} }{16} [/tex] π m²
View image AnneC