Question

A solid cylinder is of height $15cm$ and diameter $7cm$. Two equal conical holes of radius $3cm$ and height $4cm$ are cut off, one from each circular end. Find the surface area of the remaining solid.

Answer 1

Find the radius of the cylinder:

Radius = Diameter ÷ 2

Radius = 7 ÷ 2 = 3.5 cm

Find the surface area of the cylinder:

Surface area = 2πr² + 2πrh

Surface area = 2π(3.5)² + 2π(3.5)(15) = 407 cm²

Find the slanted height of the conical hole:

a² + b² = c²

c² = 3² + 4²

c² = 25

c = √25

c = 5 cm

Find the area of the base of the cone:

Area = πr²

Area = π(3)² = 198/7 cm²

Find the curved surface area of the cone:

Area = πrl

Area = π(3)(5) = 330/7 cm²

Find the total surface area:

Total Surface area = Total Surface area of cylinder - 2(base of the cone) + 2(curved surface area of the cone)

Total Surface area = 407 - 2(198/7 ) + 2(330/7) = 444.71 cm²

Answer: Total Surface area = 444.71 cm²