The lateral area of a right circular cylinder is 76 sq. cm. and its volume is 304 cu. ft.?

Question

Find its radius and altitude.

Answer 1

lateral s.a.=2pirh=76
volume=pir^2h=304
use these 2 equation, you can solve for r,h
r=38/(pih)
pi(38/pih)^2h=304
38^2pi(2)/h=304
h=38^2pi/152cm
r=1/(38pi^2/152)=152/(38pi^2)=4/pi^2cm

Answer 2

The volume of a cylinder is given by V=(area of the base)*(height)

Assume that the radius of the base is r.

V=πr^2*(height)

but for the height you know that:

lateral area=(length)*(height)

the length should be equal to the circumference of the base, thus

lateral area=2πr*h (where h is the height),so

2πrh=76 sq. cm.

also, hπr^2=304 cu. ft.


you now have two equations with two unknowns. Before you solve the system make sure you unify the units used.

1cu.ft. = 28 316.8466 cu.cm., thus

hπr^2=8608321.3664
2πrh=76

if you divide the first equation by the second then you get

(hπr^2)/(2πrh)=8608321.3664/76
r/2=113267.3864
r=226534.7728 cm (~2.2km which is a bit odd)

substituting for r in one of the equations and solving for h you get that

h=5.34*10^(-5) or
h=0.0000534 cm

The values are quite strange. Are you sure the units are correct?

Answer 3

Lateral area= 2pi r x h r=radius,h=altitude
Volume= pi r^2 x h
With these two equations, you find r
Then you can find h with either.