Question

) From a cylindrical object of diameter 70cm and height 84cm, a right solid cone having its base as one of the circular ends of the cylinder and height 84cm is removed. Calculate: The volume of the remaining solid object expressing your answer in the form ax 10, where 1< a < 10 and n is a positive integer. The surface area of the remaining solid object.​

Answer 1

The volume of the remaining solid object can be calculated by subtracting the volume of the cone from the volume of the cylinder.

The volume of the cylinder is given by: V = πr^2h = π*(70/2)^2*84 = 104,840π cm^3

The volume of the cone is given by: V = (1/3)πr^2h = (1/3)π*(70/2)^2*84 = 52,420π cm^3

Therefore, the volume of the remaining solid object is: 104,840π cm^3 - 52,420π cm^3 = 52,420π cm^3 = 52.4*10^4 cm^3

The surface area of the remaining solid object can be calculated by adding the lateral surface area of the cone to the lateral surface area of the cylinder.

The lateral surface area of the cylinder is given by: A = 2πrh = 2π*(70/2)*84 = 9,360π cm^2

The lateral surface area of the cone is given by: A = πr√(r^2+h^2) = π*(70/2)*√((70/2)^2+84^2) = 21,840π cm^2

Therefore, the surface area of the remaining solid object is: 9,360π cm^2 + 21,840π cm^2 = 31,200π cm^2 = 31.2*10^3 cm^2