A hollow spherical metal ball has internal radius 1cm. If the metal is 1/2 cm thick, find the volume of metal ( Take pi equals 22/7)
outer radius = 1.5 cm
volume (if solid metal) = (4/3)π r^3
= (4/3) π (1.5)^3
= 4.5π
Hollow part = (4/3)π(1^3 = 4π/3
so volume of metal = (9/2)π - (4/3)π
= (19/6)π
or appr. 9.95 , (nobody uses 22/7 for π, we all have calculators)
To find the volume of metal in the hollow spherical ball, we need to subtract the volume of the inner sphere from the volume of the outer sphere.
First, let's calculate the volume of the inner sphere with a radius of 1cm:
Volume of inner sphere = (4/3) * pi * radius^3
= (4/3) * (22/7) * (1cm)^3
= (4/3) * (22/7) * (1)^3
= (4/3) * (22/7) * 1
= (4/3) * 22/7
= (88/21) cm^3
Now, let's calculate the radius of the outer sphere. The outer radius is the sum of the inner radius (1cm) and the thickness (1/2 cm):
Outer radius = Inner radius + Thickness
= 1cm + 1/2 cm
= 3/2 cm
Next, we'll calculate the volume of the outer sphere with a radius of 3/2 cm:
Volume of outer sphere = (4/3) * pi * radius^3
= (4/3) * (22/7) * (3/2 cm)^3
= (4/3) * (22/7) * (27/8) cm^3
= (4/3) * (66/8) * (27/1) cm^3
= (88/3) * (27/1) cm^3
= (2376/3) cm^3
= 792 cm^3
Finally, subtract the volume of the inner sphere from the volume of the outer sphere to get the volume of the metal:
Volume of metal = Volume of outer sphere - Volume of inner sphere
= 792 cm^3 - 88/21 cm^3
= (792*21 - 88)/21 cm^3
= 16584/21 cm^3
= 788 cm^3
Therefore, the volume of the metal in the hollow spherical ball is 788 cm^3.