a closed tin is in the shape of acylinder of diameter 10cm and height 15cm.use the value 3.14 for pie to find a)the total surface area of the tin b)the value of the tin to the nearest naira if tin plate cost 450 per m2
2*3.14*5 (5 plus 15)
31.4 (20)
628cm^20th total surface area
pi, not pie!
2pi(r^2+rh) = 2pi(25+75) = 200pi
Now just multiply that are by the cost, which is .0450/cm^2
To find the total surface area of the closed tin, we need to calculate the areas of the top and bottom circles, as well as the lateral surface area.
a) The formula for the area of a circle is given by:
A = πr^2
Given that the diameter (d) of the tin is 10 cm, we can calculate the radius (r) by dividing the diameter by 2:
r = d/2 = 10 cm / 2 = 5 cm
Now we can find the areas of the top and bottom circles:
A_circle = πr^2
= 3.14 * (5 cm)^2
= 3.14 * 25 cm^2
= 78.5 cm^2
The lateral surface area of a cylinder is given by:
A_lateral = 2πrh
Given that the height (h) of the tin is 15 cm, we can calculate the lateral surface area:
A_lateral = 2 * 3.14 * 5 cm * 15 cm
= 3.14 * 150 cm^2
= 471 cm^2
Finally, the total surface area (A_total) is the sum of the areas of the top and bottom circles, and the lateral surface area:
A_total = 2 * A_circle + A_lateral
= 2 * 78.5 cm^2 + 471 cm^2
= 157 cm^2 + 471 cm^2
= 628 cm^2
The total surface area of the tin is 628 cm^2.
b) To find the value of the tin, we need to calculate the cost of the tin plate per cm^2 and multiply it by the total surface area.
Given that the tin plate costs ₦450 per m^2, we first need to convert it to ₦ per cm^2.
1 m^2 = 100 cm * 100 cm = 10,000 cm^2
₦450/m^2 = ₦450/10,000 cm^2 = 0.045 ₦/cm^2
Now, we can calculate the value of the tin:
Value = Cost per cm^2 * Total surface area
= 0.045 ₦/cm^2 * 628 cm^2
= 28.26 ₦ (rounded to 2 decimal places)
Therefore, the value of the tin to the nearest naira is ₦28.26.
To find the total surface area of the closed tin, we need to calculate the surface area of the top and bottom circles (bases) and the curved surface area (lateral surface).
a) To find the surface area of the top and bottom circles, we will use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius. In this case, we are given the diameter, so we need to find the radius first.
Given:
Diameter (d) = 10 cm
To find the radius (r), we divide the diameter by 2:
r = d/2 = 10/2 = 5 cm
Now, we can calculate the area of the top and bottom circles:
Area of each circle = πr^2 = 3.14 * 5^2 = 3.14 * 25 = 78.5 cm^2 (rounded to one decimal place)
Since the tin has a top and bottom, the total area of the circles is twice the area of one circle:
Total area of the circles = 2 * 78.5 = 157 cm^2
b) To find the curved surface area, we will use the formula for the lateral surface area of a cylinder, which is A = 2πrh, where A is the surface area, r is the radius, and h is the height.
Given:
Radius (r) = 5 cm
Height (h) = 15 cm
Curved surface area = 2πrh = 2 * 3.14 * 5 * 15 = 471 cm^2 (rounded to the nearest whole number)
Now, to calculate the total surface area, we add the areas of the circles and the curved surface area:
Total surface area = Total area of the circles + Curved surface area
Total surface area = 157 cm^2 + 471 cm^2 = 628 cm^2
Now, to find the value of the tin to the nearest naira, we need to calculate the cost based on the cost of the tin plate per m^2.
Given:
Cost of tin plate = 450 Naira per m^2
To find the value of the tin, we need to convert the surface area from cm^2 to m^2, and then multiply it by the cost per m^2:
Surface area in m^2 = Surface area in cm^2 / 10,000 (since 1 m^2 = 10,000 cm^2)
Surface area in m^2 = 628 / 10,000 = 0.0628 m^2 (rounded to four decimal places)
Value of the tin = Surface area in m^2 * Cost of tin plate
Value of the tin = 0.0628 * 450 = 28.26 Naira (rounded to two decimal places)
Therefore, the value of the tin to the nearest naira is 28.26 Naira.