V = 42π2 – πr2, help me ):?
this question confuses me, it says:
A cylider of radius r and height h is such that the sum of the radius and height is 42
a) show that the volume of the cylinder is given by V = 42 π2 – π r3
what does π r3 find? since V of cylinder = hπ r2, and 42 is h + r does π r3 = r? it doesnt make sense to me
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Verified answer
V of a cylider = π r^2 h
r + h = 42
h = 42 - r
Use (h = 42 - r) in V instead of h.
V = π r^2 (42 - r) =
42 π r^2 - π r^3
Edit :
You wrote V = 42 π2 – π r3
and it's wrong, you should write V = 42π r2 – π r3
Hi Fred,
Nothing really to get confused,
R+H=42
we know that Volume of Cylinder = Ï r^2h
substitute h=42-R in Volume
Ï r^2(42-r)
=>42 Ï r^2 - Ï r^3
Proved
====
h=42-r
V=h Ï r2
=(42-r) Ï r2
=42 Ï r2 - Ï r3