Question

A solid metal sphere of diameter 30cm is melted down and recast into a hollow metal pipe of internal radius of 3.5cm and external radius of 4 cm. In the process, 10% of the metal is lost. Giving your answer in terms of π calculate
A) The volume of the metal in the sphere
B)The volume of the metal used to make the pipe
C) The cross-sectional area of the metal in the pipe
D) Calculate the length of the pipe in metres

Answer 1

Using general area and volume formulas:

a) V = π*3,375cm^3

b) V'  = π*3,037.5 cm^3

c) A = π*7.5cm^2

d) The length of the pipe is 405cm.

How to get the volume of the sphere?

Remember that a sphere of radius R has a volume:

V = π*R^3

In this case, the diameter is 30cm, so the radius (half of that) is:

R = 30cm/2 = 15cm

So the volume is:

V = π*(15cm)^3 = π*3,375cm^3

b) Ok, 10% of the metal is lost when making the pipe, then the volume of the pipe will be the 90% of the above volume:

V' = π*3,375cm^3*(0.9) = π*3,037.5 cm^3

c) It will b a ring of internal radius of 3.5cm and external radius of 4cm.

The area of a ring with internal radius r and external radius R is:

A = 2*π*(R^2 - r^2)

A = 2*π*((4cm)^2 - (3.5cm)^2) = π*7.5cm^2

d) The length of the pipe will be h, and we must have that the height times the cross-sectional area is equal to the volume, then:

(π*7.5cm^2)*h = π*3,037.5 cm^3

7.5*h = 3,037.5 cm

h = 3,037.5 cm/7.5 = 405cm

The length of the pipe is 405cm.

If you want to learn more about volume:

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