Three-dimensional Solids Right Circular Cone

The total surface area of a right circular cone of slant height 13 cm is 90π cm2. Calculate:  

(i) its radius in cm
(ii) its volume in cm3 [Take π = 3.14]  

A solid metal sphere is cut through its center into 2 equal parts. If the diameter of the sphere is`3 1/2` cm, find the total surface area of each part correct to two decimal places. 

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5cm. Find the number of sphere formed.

A solid, consisting of a right circular cone standing one a hemisphere, is placed upright in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of
the hemisphere is 2 cm and the height of cone is 4 cm. Give your answer to the nearest cubic centimeter.

Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm 

The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:
(i) radius of the floor.
(ii) height of the tent
(iii) length of the canvas required to cover this conical tent if its width is 2 m. 

Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitching’s. Also. Find the cost of the canvas at the rate of Rs. 24 per metre.

The radii of the internal and external surface of a metallic spherical. It is melted and recast into a solid right circular cone of height 32 cm. Find the diameter of the base of the cone.