A closed tin is in the shape of a cylinder of diameter 10cm and height 15cm.Use the value 3.14 for pier to find:
a)the total surface area of the tin,
b)the value of the tin to the nearest naira if tin plate costs 450 per m2.
The surface area consists the area of 2 equal circles + the area of a rectangle
= 2Pr^2 + 2πrh
= 2(π(5^2)) + 2π(5)(10)
=.... you do the arithmetic
once you have the total area, multiply that by the cost per square unit.
Careful here, notice my answer above will be in cm^2, but the cost is in m^2
so you have to convert.
Thanks this question has been bugging me for weeks now.
I still dont understand
Please can someone explain this to me
Slightly bad but very good job
To find the total surface area of the tin, we need to calculate the areas of all the components that make up the surface.
a) The total surface area of the tin includes the area of the curved side, as well as the areas of the top and bottom circles.
1. Area of the curved side: The side of the tin is in the shape of a cylinder, which can be represented as a rectangle that is rolled into a circle. The height of the cylinder is given as 15 cm. The circumference of the cylinder can be calculated using the formula: C = πd, where d is the diameter.
So, C = π * 10 cm = 31.4 cm
The height of the cylinder corresponds to the length of the rectangle, and the circumference corresponds to its width. Thus, the area of the curved side is given by: A = length * width = height * circumference.
A = 15 cm * 31.4 cm = 471 cm²
2. Area of the top and bottom circles: The area of a circle can be calculated using the formula: A = πr², where r is the radius (half of the diameter).
The radius is given as 10 cm / 2 = 5 cm.
So, the area of each circle is: A = π * (5 cm)² = 78.5 cm²
Since there are two circles (top and bottom), the total area of both circles is: 2 * 78.5 cm² = 157 cm²
Finally, to find the total surface area of the tin, we add together the areas of the curved side, top circle, and bottom circle:
Total surface area = Area of curved side + Area of top circle + Area of bottom circle
Total surface area = 471 cm² + 157 cm²
Total surface area = 628 cm²
b) To find the value of the tin to the nearest naira, we need to calculate the cost per square centimeter and then multiply it by the total surface area.
1. Cost per square centimeter: We are given that the tin plate costs 450 per m², which means we need to convert that to cost per square centimeter. There are 10,000 square centimeters in one square meter (1 m² = 10,000 cm²). Therefore, the cost per square centimeter is: 450 / 10,000 = 0.045 naira/cm².
2. Total cost of the tin: To calculate the cost of the tin, we multiply the cost per square centimeter by the total surface area in square centimeters.
Total cost = Total surface area * Cost per square centimeter
Total cost = 628 cm² * 0.045 naira/cm²
Calculating this multiplication will give us the final value of the tin to the nearest naira.