From a solid metallic cylinder of height 24 cm, a cone of same height

1.	From a solid metallic cylinder of height 24 cm, a cone of same height and same base (ascylinder) is taken out. The density of the metal is 10 gm per cm'. If the mass of the remainingportion of the cylinder is 24.64 kg, then find the cost required to paint the remaining portionat a rate of Rs 3 per 440 cm?.2.
Answer» volume of the remaining part of the solid = (pi)r^2 h - 1/3 (pi)r^2 h = 2/3 (pi) r^2 h Density is given as 10gm/cm3 ,meaning mass of every 1cm3=10gms It is given that mass of remaining portion = 24.64kg = 24640gms then,2/3 * 22/7 r^2 24* 10 =24640r^2 = 49r = 7 Slant height of cone l= sqrt[(24)^2 + (7)^2] = sqrt(625) = 25 surface area of the remaining portion = 2 pi r h + pi r^2 + pi r l= pir(2h + r + l)= 227/7(224 + 7 + 25)= 22(48 + 32)= 22(80)= 1760 cm^2 Cost of painting per 440 cm^2 = Rs 3Cost of painting 1760 cm^2= 17603/440= 4*3= Rs 12

From a solid metallic cylinder of height 24 cm, a cone of same height and same base (ascylinder) is taken out. The density of the metal is 10 gm per cm'. If the mass of the remainingportion of the cylinder is 24.64 kg, then find the cost required to paint the remaining portionat a rate of Rs 3 per 440 cm?.2.

Answer»

volume of the remaining part of the solid = (pi)r^2 h - 1/3 (pi)r^2 h

= 2/3 (pi) r^2 h

Density is given as 10gm/cm3 ,meaning mass of every 1cm3=10gms

It is given that mass of remaining portion = 24.64kg = 24640gms

then,2/3 * 22/7 *r^2 *24* 10 =24640r^2 = 49r = 7

Slant height of cone l= sqrt[(24)^2 + (7)^2] = sqrt(625) = 25

surface area of the remaining portion = 2 pi r h + pi r^2 + pi r l= pi*r(2h + r + l)= 22*7/7(2*24 + 7 + 25)= 22(48 + 32)= 22(80)= 1760 cm^2

Cost of painting per 440 cm^2 = Rs 3Cost of painting 1760 cm^2= 1760*3/440= 4*3= Rs 12