Answer:
The volume of metal in a can is 13.8 cm³.
Explanation:
Given that,
Height = 10 cm
Diameter = 4 cm
Thickness at bottom = 0.3 cm
Thickness at side = 0.05 cm
The change in radius = 0.05 cm
The total change in height is
[tex]dh=0.3+0.3 = 0.6\ cm[/tex]
The volume V of a cylinder in term of height and radius r
Using formula of volume
[tex]V(h,r)=\pi\times r^2\times h[/tex]
On differentiated with respect to r
[tex]\dfrac{dV}{dr}=2\pi r h[/tex]...(I)
On differentiated with respect to h
[tex]\dfrac{dV}{dh}=\pi r^2[/tex]
The total differentialis,
[tex]dV=\dfrac{dV}{dr}dr+\dfrac{dV}{dh}dh[/tex]
Put the value into the formula
[tex]dV=2\pi rh dr+\pi r^2 dh[/tex]
Put the value into the formula
[tex]dV=2\pi\times2\times10\times0.05+\pi\times(2)^2\times0.6[/tex]
[tex]dV=13.8\ cm^3[/tex]
Hence, The volume of metal in a can is 13.8 cm³.
