Question

The given solid is the cylinder surmounted by a cone .The diameter of the base of the cylinder is 6 cm,the height of the cone is 4cm and the total height of the solid is 25 cm.Find:
1)The volume of the solid.
2)The curved surface area of the solid.

Answer 1

The diameter of both Cylinder and Cone = 6 cm

The Radius of both Cylinder and Cone = r = 3 cm

Height of cone = h = 4 cm

Total height = 25 cm

Height of Cylinder = H = 25 - 4 = 21 cm

Volume of Solid:

Volume of solid = Volume of cylinder + Volume of Cone

                         =  π r^2 H  + π r^2 (h/3)

                         = π r^2 (H + h/3)

                          = (22/7)(3^2) ( 21+ 4/3)

    Volume =    631.71 cubic cm

The Curved Surface Area of Solid:

= Curved surface Area of Cylinder + Curved surface Area of Cone

= 2 π r H + π r sqrt{h^2 + r^2}    ( sqrt represents square root of the value)

=  π r [ 2H +  sqrt{h^2 + r^2}

=  (22/7) (3) [ 2(21) +  sqrt{4^2 + 3^2}

= 443. 14 square cm