if the radius and height of a cone both are increased by 10%. how much is the volume increased.
old radius -- x
old height -- h
old volume = (1/3)πr^2 h
new radius = 1.1r
new height = 1.1h
new volume = (1/3)π (1.1r)^2 (1.1)h
= 1.1^3 (1/3)πr^2 h
ratio of increase = 1.1^3 (1/3)πr^2 h/((1/3)πr^2 h)
= 1.1^3 = 1.331
there is a 33.1% increase
The last ans we get is 1.331 and then how do we get 33.1%
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To find the increase in volume when both the radius and height of a cone are increased by 10%, we can follow these steps:
1. Calculate the original volume of the cone using the formula V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius, and h is the height.
2. Increase the radius and height of the cone by 10%. To do this, multiply the original radius by 1.1 and the original height by 1.1.
3. Calculate the new volume of the cone using the same formula mentioned in step 1, but with the increased radius and height.
4. Find the difference between the new volume and the original volume. This will give you the increase in volume.
Let's calculate the increase in volume using an example:
Assume the original radius of the cone is 5 units and the original height is 8 units.
1. Original volume:
V = (1/3) * π * 5^2 * 8
V = (1/3) * 3.14159 * 25 * 8
V ≈ 209.4395 units^3
2. Increased radius and height:
New radius = 5 * 1.1 = 5.5 units
New height = 8 * 1.1 = 8.8 units
3. New volume:
V = (1/3) * π * 5.5^2 * 8.8
V = (1/3) * 3.14159 * 30.25 * 8.8
V ≈ 331.2219 units^3
4. Increase in volume:
Increase in volume = New volume - Original volume
Increase in volume = 331.2219 - 209.4395
Increase in volume ≈ 121.7824 units^3
Therefore, the volume of the cone increases approximately by 121.7824 units^3 when both the radius and height are increased by 10%.