Question

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 N4 500
Per m ​

Answer 1

To find the total surface area of the tin, we need to consider the curved surface area of the cylinder (excluding the top and bottom) and the areas of the two circular bases.

Curved Surface Area of the Cylinder:

The formula for the curved surface area of a cylinder is 2πrh, where r is the radius and h is the height.

Given that the diameter is 10 cm, the radius (r) is half of that, which is 10/2 = 5 cm.

Substituting the values, the curved surface area = 2 * 3.14 * 5 * 15 = 471 cm².

Area of the Circular Bases:

The formula for the area of a circle is πr², where r is the radius.

The radius (r) is 5 cm.

Substituting the value, the area of one circular base = 3.14 * 5² = 78.5 cm².

Since there are two circular bases, the total area of the bases = 2 * 78.5 = 157 cm².

Total Surface Area:

Adding the curved surface area and the area of the bases, the total surface area of the tin = 471 + 157 = 628 cm².

b) To determine the value of the tin, we need to convert the surface area from cm² to m² since the cost of tin plate is given per square meter.

1 m² is equal to 10,000 cm². Therefore, the surface area of the tin in square meters is 628/10,000 = 0.0628 m².

Given that the cost of tin plate is N4,500 per square meter, we can calculate the value of the tin:

Value of the tin = Surface area in square meters * Cost per square meter

Value of the tin = 0.0628 * N4,500 = N282.60 (rounded to the nearest 10 Naira)

Therefore, the value of the tin to the nearest 10 Naira is N280.

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