13 solid spheres of radius 4 m, 14 solid cones of radius 3 m, height 5 m and 17 solid cylinders of r

M4maths Previous Puzzles

11 May 2018 Volume

13 solid spheres of radius 4 m, 14 solid cones of radius 3 m, height 5 m and 17 solid cylinders of radius 2m and height 6m are melted to form a bigger solid cone of height 1500 cm. What is the radius of this bigger solid cone in meters?

OPtion

1) 10.59
2) 18.59
3) 10.73
4) 10.90
5) 18.95
6) 18.64
7) 17.77
8) 17.95
9) 17.09
10) None of the above

Solution

Vol of Sphere = (4/3)*Pi*r^3
Vol. of Cylinder = Pi*r^2*h
Vol. of cone = (1/3)*Pi*r^2*h


Volume of 13 solid spheres = 13 * 268.19 = 3486.48

Volume of 14 solid cones = 14 * 47.14 = 660


Volume of 17 solid cylinders = 17 * 75.43 = 1282.29

Total Volume = 5428.762 m

Radius of larger cone = [(3*Total Volume /Pi*h)]^1/2 = ~ 18.59 m

Correct Option: 2 Best Solution (0)