Find the approximate increase in the surface area of a spherical balloon if it's radius increases from 4cm to 4.025cm
The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius.
For the first scenario, when the radius is 4 cm:
A1 = 4π(4 cm)^2
A1 ≈ 201.06 cm^2
For the second scenario, when the radius is 4.025 cm:
A2 = 4π(4.025 cm)^2
A2 ≈ 204.05 cm^2
The approximate increase in surface area is:
ΔA ≈ A2 - A1
ΔA ≈ 204.05 cm^2 - 201.06 cm^2
ΔA ≈ 2.99 cm^2
Therefore, the approximate increase in surface area of the spherical balloon is 2.99 cm^2.
To find the approximate increase in the surface area of a spherical balloon, we can use the formula for the surface area of a sphere:
Surface Area = 4πr^2
Let's calculate the surface area of the balloon with a radius of 4 cm:
Surface Area1 = 4π(4)^2
Surface Area1 = 4π(16)
Surface Area1 ≈ 64π cm^2
Now, let's calculate the surface area of the balloon with a radius of 4.025 cm:
Surface Area2 = 4π(4.025)^2
Surface Area2 = 4π(16.2)
Surface Area2 ≈ 64.6π cm^2
To find the increase in surface area, subtract the initial surface area from the final surface area:
Increase in Surface Area ≈ Surface Area2 - Surface Area1
Increase in Surface Area ≈ 64.6π cm^2 - 64π cm^2
Increase in Surface Area ≈ 0.6π cm^2
Therefore, the approximate increase in the surface area of the spherical balloon is approximately 0.6π cm^2.