A closed tin of milk has diameter 10cm and height 16cm. Find the total surface of the tin.(take π to be 22/7)
d = diameter
r = radius
Surface area:
A = 2 area of circles + 1 area of rectangle = 2 r² π + 2 r π h = 2 r π ( r + h )
r = d / 2 = 10 / 2 = 5 cm
A = 2 ∙ 5 ∙ 22 / 7 ∙ ( 5 + 16 ) = 2 ∙ 5 ∙ 22 ∙ 21 / 7 = 660 cm²
OR
A = 2 area of circles + 1 area of rectangle = 2 d² π / 4 + d π h =
d² π / 2 + d π h = d π ( d / 2 + h )
10 ∙ ( 22 / 7 ) ∙ ( 10 / 2 + 16 ) = 220 / 7 ∙ ( 5 + 16 ) =
220 ∙ 21 / 7 = 4620 / 7 = 660 cm²
2πr(h+r)
2π×10(16+10)
=2×22/7×10(26)
=44×260/7
=11440/7
=1634.3
As = 2(pi*r^2)+2pi*r*h = 2(3.14*5^2) + 6.28*5*16 = 659.5 cm^2.
To find the total surface area of the tin, we need to consider the base and the curved surface area.
1. Base Area: The base of the tin is circular, and the formula to find the area of a circle is A = πr², where r is the radius of the circle.
- The diameter of the tin is given as 10 cm, so the radius is half of the diameter, which is 10/2 = 5 cm.
- Plugging the radius (r = 5 cm) into the formula, we get the base area as A = π(5 cm)².
2. Curved Surface Area: The curved surface of the tin can be thought of as a rectangle that has been wrapped around the curved surface of the tin.
- The height of the tin is given as 16 cm. The length of the rectangle is the same as the circumference of the circular base.
- The circumference of a circle is given by C = 2πr, where r is the radius.
- Plugging the radius (r = 5 cm) into the formula, we get the circumference as C = 2π(5 cm).
- The length of the rectangle is equal to the circumference, so it is 2πr.
- The width of the rectangle is the height of the tin, which is 16 cm.
To calculate the surface area, we add the base area and the curved surface area:
Surface Area = Base Area + Curved Surface Area
Surface Area = π(5 cm)² + 2π(5 cm)(16 cm)
Now, substitute the value of π as 22/7 and calculate:
Surface Area = (22/7)(5 cm)² + 2(22/7)(5 cm)(16 cm).
Evaluate this expression to get the answer.