Question

Cylinder of height 30 cm and radius 7 cm a conical cavity of height 24cm and of base radius 7 cm is filled out find the volume and total surface area of the remaining solid

Answer 1

Radius of the cylinder = 6 cm Height of the cylinder = 8 cm Volume of the solid cylinder = πr2h = 22/7 × 6 × 6 × 8 = 905.14 cm2 Radius of the base of the conical cavity = 6 cm Height of the conical cavity = 8 cm Volume of the conical cavity = 1/3 πr2h = 1/3 × 22/7 × 6 × 6 × 8 = 301.71 cm2Volume of the remaining solid = 905.14 - 301.71 = 603.43 cm2 Total surface area of the remaining solid = CSA of the cylinder + CSA of the conical cavity + Area of the base of the cylinder CSA of the cylinder = 2πrh = 2π × 6 x 8 = 96 π CSA of the conical cavity = πrl = πr√[(r)2 + (h)2] = π x (6)2 x √[(6)2 + (8)2] = π x (6)2 x √100 = π x 36 x 10 = 360 π Area of the base of the cylinder = π r2 = π (6)2 = 36 π Total surface area of the remaining solid = 96 π + 360 π + 36 π = 492 π = 492 x 3.1412 = 1545.4704 cm2

Answer 2

the answer is 1545.47 cm square