Question

A hole with a diameter of 3.5 cm is drilled through a square metal nut of thickness 4 cm and length 6 cm. What is the surface area?

Answer 1

Answer:

192.75 cm²

Step-by-step explanation:

Find the radius:

Radius = Diameter ÷ 2

Radius = 3.5 ÷ 2 = 1.75 cm

Find the inner surface area of the hole created by the drill:

Surface area = 2πrh

Surface area = 2π(1.75)(4) = 44 cm²

Find the area of the top and bottom with the hole drilled:

Area = 2(Length x Length - πr²)

Area = 2(6 x 6 - π(1.75)² )

Area = 52.75 cm²

Find the area of the 4 sides:

Area = 4(Length x thickness)

Area = 4(6 x 4 )

Area = 96 cm²

Find the total surface area:

Total surface area = 44 + 52.75 + 96 = 192.75 cm²

Answer: 192.75 cm²