Answer :
Answer
a) Volume of the cylinder = 80π cm³ = 251.43 cm³
b) New volume of the cylinder when radius triples = 720 π cm³ = 2262.86 cm³
The new volume = 9 × (The original volume) when the radius is tripled.
c) New volume of the cylinder = 20π cm³ = 62.86 cm³
The new volume = ¼ × (The original volume) when the radius is halved.
OR
The original volume = 4 × (The new volume) when the radius is halved.
Explanation
The volume of a cylinder is given as
Volume of a cylinder = πr²h
where
π = pi
r = radius of the cylinder
h = height of the cylinder
a) Volume of a cylinder, radius = 4 cm, height = 5cm
Volume of a cylinder = πr²h
Volume of the cylinder = π (4²) (5) = 80π cm³
b) The new volume of the cylinder when the radius is tripled.
Original radius = 4 cm
When it is tripled,
New radius = 3 (4 cm) = 12 cm
Height = 5 cm
Volume of a cylinder = πr²h
Volume of a cylinder = π (12²) (5) = 720π cm³
We can see that the new volume is 9× the original volume.
c) The new volume of the cylinder when the radius is halved.
Original radius = 4 cm
When it is halved,
New radius = ½ (4 cm) = 2 cm
Volume of a cylinder = πr²h
Volume of a cylinder = π (2²) (5) = 20π cm³
We can see that the new volume is ¼× the original volume.
Or the original volume is 4 × the new volume when the radius is halved.
Hope this Helps!!!!
