A close tin is in the shape of a cylinder of diameter 10cm and height 15cm.use the value of 3.14 for pie find
a total surface of a tin.
b. The volume of the tin to the nearest 10 naira if the tin plate costs 4,500naira per m2
a) The total surface area of the tin can be found by adding the area of the top and bottom circles (which are the same) and the area of the curved part of the cylinder:
Area of top and bottom circles = πr^2 = 3.14 x (10/2)^2 = 78.5 cm^2 (rounded to 1 decimal place)
Area of curved part = 2πrh = 2 x 3.14 x (10/2) x 15 = 942 cm^2 (rounded to the nearest whole number)
Total surface area = 2 x 78.5 + 942 = 1099 cm^2 (rounded to the nearest whole number)
b) The volume of the tin can be found using the formula V = πr^2h:
V = 3.14 x (10/2)^2 x 15 = 353.25 cm^3 (rounded to 2 decimal places)
Converting this to m^3:
353.25 cm^3 = 0.00035325 m^3
Multiplying by the cost per square meter of tin plate (which is 4,500 naira), we get:
Cost = 0.00035325 x 4,500 = 1.59 naira (rounded to 2 decimal places)
Therefore, the volume of the tin to the nearest 10 naira is 350 naira (rounded up from 1.59 to the nearest 10 naira).
To find the total surface area of the tin, we'll need to calculate the lateral surface area of the cylinder and add it to the areas of the two circular bases.
a) Lateral Surface Area:
The formula for the lateral surface area of a cylinder is given by A = 2πrh, where r is the radius and h is the height.
Given:
Diameter = 10 cm
Radius (r) = Diameter/2 = 10/2 = 5 cm
Height (h) = 15 cm
Substituting the values:
Lateral Surface Area (A) = 2 × 3.14 × 5 × 15 cm²
= 471 cm²
b) Circular Bases:
The formula for the area of a circle is given by A = πr².
Base Area = 2 × π × r²
= 2 × 3.14 × (5 cm)²
= 157 cm²
Total Surface Area = Lateral Surface Area + 2 × Base Area
= 471 cm² + 2 × 157 cm²
= 471 cm² + 314 cm²
= 785 cm²
b) Volume:
The formula for the volume of a cylinder is given by V = πr²h.
Volume (V) = π × (5 cm)² × 15 cm³
= 3.14 × 25 cm² × 15 cm
= 1177.5 cm³
To convert cm³ to m³ (since the cost of the tin plate is given per m²):
1 m³ = (100 cm) x (100 cm) x (100 cm) = 1,000,000 cm³
Volume (V) = 1177.5 cm³ / 1,000,000 = 0.0011775 m³
Now, let's find the cost:
Tin plate cost = 4,500 Naira/m²
Cost = Tin Plate Cost × Surface Area
= 4,500 Naira/m² × 785 cm²
= 4,500 Naira/m² × 0.0785 m²
= 353.25 Naira
Therefore, the volume of the tin is approximately 0.0012 m³ and the cost of the tin plate is approximately 353.25 Naira.