A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape - Maths - Surface Areas and Volumes

Question

A solid cylinder of diameter 12 cm and height 15 cm is melted
and recast into toys with the shape of a right circular cone
mounted on a hemi - sphere of radius 3cm If the height of the toy
is 12 cm Find the number of toys so formed

Ajanta Trivedi · Accepted Answer

the diameter of the base of the cylinder = 12 cm the radius of the cylinder r = 12/2 = 6 cm the height of the cylinder h = 15 cm the volume of the cylinder = $π r^{2} h = 6^{2} * 15 π = 540 π c m^{3}$

the toy are in the shape of cone mounted on hemisphere the radius of the hemisphere r1 = 3 cm volume of the hemispherical part = $\frac{2}{3} π {r_{1}}^{3} = \frac{2}{3} π * 3^{3} = 18 π c m^{3}$ total height of the toy = 12 cm height of the cone = 12-3 =9 cm radius of the cone is same as radius of the hemisphere radius of the cone r1 = 3 cm volume of the cone = $\frac{1}{3} π {r_{1}}^{2} h = \frac{1}{3} π * 3^{2} * 9 = 27 π c m^{3}$ total volume of the toy = volume of the cone + volume of the hemisphere $= 18 π + 27 π = 45 π c m^{3}$ let x number of toys can be made therefore the volume of the x toys = volume of the cylinder $x * 45 π = 540 π x = \frac{540}{45} = 12$ thus 12 toys can be made hope this helps you

A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemi - sphere of radius 3cm. If the height of the toy is 12 cm . Find the number of toys so formed.