An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8cm. The cylindrical part is 240cm high and the conical part is 36cm high. Find the weight of the pillar if one cubic cm of iron weighs 7.8 grams.
Let r1 cm and r2 cm denote the radii of the base of the cylinder and cone respectively. Then,
r1=r2=8 cm
Let h1 and h2 cm be the heights of the cylinder and the cone respectively. Then
h1=240cm;h2=36cm
volume of Cylinder =πr21h136cm3=(π×8×8×240)cm3=(π×64×240)cm3
volume of Cone =13πr22h2cm3=(13π×8×8×36)cm3
Total volume of the iron = volume of the cylinder + Volume of the cone
=(π×64×240+13π×64×36)cm3=227×64×252cm3=22×64×36cm3
total weight of the pillar = volume × Weight per cm3
(22×64×36)×7.8gms=395.3664kg