ig. 19.9 A closed tin is in the shape of a cylinder of diameter 10 cm and height 15 cm. Use the value 3.14 for π to find: a The total surface area of the tin. b The value of the tin to the nearest 10 naira, if tin plate costs 4500 per m^2
a)
Total surface area of the tin = 2πr(r + h) + πr^2
Where r is the radius of the base of the cylinder and h is the height of the cylinder.
Given:
Diameter = 10 cm, so radius, r = 10/2 = 5 cm
Height, h = 15 cm
Total surface area = 2 x 3.14 x 5(5 + 15) + 3.14 x 5^2
= 2 x 3.14 x 5 x 20 + 3.14 x 25
= 314 + 78.5
= 392.5 cm^2
b)
Area of tin plate = Total surface area of the tin
= 392.5 cm^2
Converting cm^2 to m^2:
1 cm^2 = 0.0001 m^2
So, 392.5 cm^2 = 392.5 x 0.0001 m^2 = 0.03925 m^2
Cost of the tin plate = Area x Cost per m^2
= 0.03925 x 4500
= 176.63 Naira
Therefore, the value of the tin to the nearest 10 Naira is 180 Naira.