the height of a right circular cylinder is three times the radius of its base. If the height would have been four times the radius, the volume would be 1078cc more than its previous volume. Find the volume and the total surface area.
Answers
Answer:
The volume of the cylinder is 3234cc
and the Total surface area of the cylinder is 1232 cm²
Step-by-step explanation:
Let the height of the cylinder be 'h'
and the radius of the cylinder be 'r'
Given that h = 3r
We know that for a cylinder, Volume = πr²h
where r is the radius of the cylinder
and h is the height of the cylinder
According to the condition given here, that is h = 3r,
Therefore, Volume = πr²h = πr²(3r) = 3πr³
Now, the second condition states that if h = 4r , new V = 1078 + V --(i)
New Volume = πr²h = πr²(4r) = 4πr³
Substituting the values in equation (i), we get
4πr³ = 1078 + 3πr³
=> 4πr³ - 3πr³ = 1078
=> πr³ = 1078
We know that π = 22/7
=> (22/7)r³ = 1078
=> r³ = 1078 * (7/22)
=> r³ = 1078 * (7/22)
=> r = 7
When r = 7, h = 3r = 3*7 = 21
Therefore, volume of the cylinder = πr²h = (22/7)* 7² * 21
= 3234cc
We know that the total surface area for a cylinder = 2πrh + 2πr² = 2πr(h+r)
On substituting the values, we get,
Total surface area = 2*(22/7)*7 *(21 + 7)
= 44 * 28
= 1232 cm²
Therefore, the volume of the cylinder is 3234cc
and the Total surface area of the cylinder is 1232 cm²