the area of the base of the cylinder is 45 square inches and it's height is 10 inches. A vine has the same area of its base and the same height. what is the volume of the cone ?

Accepted Solution

Answer:The volume of cone = 5.369 inches³Step-by-step explanation:Given as :The curved surface area of cylinder = 45 inches²The height of cylinder = 10 inches Now,  curved surface area of cylinder = 2 × [tex]\pi[/tex] × r × hwhere r is radiusand h is heightSo , 2 × [tex]\pi[/tex] × r × h =  45 inches²So, r = [tex]\frac{45}{20\pi }[/tex]Now, Cone have same base are and height Let The volume of cone = v Since The volume of cone = [tex]\frac{1}{3}[/tex] ×[tex]\pi[/tex]×r²×h So,  The volume of cone =[tex]\frac{1}{3}[/tex]  × [tex]\pi[/tex]× ([tex]\frac{45}{20\pi }[/tex])² × 10Or,  The volume of cone = [tex]\frac{945}{176}[/tex]       The volume of cone = 5.369 inches³ Answer