f2 math area and volume

1.
The area of the curved surface and volume of a cylinder are 4π (m²) and 10π (m³) respectively. Find theradius and the height of the cylinder.

Let r (m) and h (m) be the radius and the height of the cylinder respectively.

2πrh = 4π ...... (1)
πr²h = 10π ...... (2)

(2)/(1):
r/2 = 10/4
r = 5

Put r = 5 into (1) :
2π(5)h = 4π
10h = 4
h = 2/5

Hence,
radius of the cylinder = 5 m
height of the cylinder = 2/5 m


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2. The water in a rectangular tank with a base of 20m by 25mis pumped into a cylindrical tank of base radius 10m through a pipe of diameter60cm at a rate of 1.5m/s.
a) What is the volume of water delivered by the pipe in 1 hour?
b) After 1 hour, find the fall of water level in the rectangular tank.
c) After 1 hour, find the rise of water level in the cylindrical tank.

a)
Radius of the pipe
= 60/2 cm
= 30/100 m
= 0.3 m

Volume of water delivered by the pipe in 1 hour
= π x (0.3)² x (1.5 x 3600) m³
= 486π m³
≈ 1530 m³

b)
The fall of water level in the rectangular tank after 1 hour
= 486π / (20 x 25) m
= 0.972π m
≈ 3.05m

c)
The rise of water in the cylindrical tank after 1 hour
= 486π / (π x 10²)
= 4.86 m