Question

Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4√t cm^3. After 100 seconds, the radius of the balloon is?

a) 10 cm
b) 20 cm
c) 25 cm
d) 50 cm

Answer 1

To find the radius of the spherical balloon after t = 100 seconds, we use the volume V = 40 cm^3 and solve for R in the volume formula of a sphere, resulting in an approximate radius of 2.04 cm.

Step-by-step explanation:

To find the radius of the spherical balloon after 100 seconds, we use the given volume formula V = 4√t cm3. According to this formula, when t = 100, V = 4√100 cm3 = 4(10) cm3 = 40 cm3. The volume of a sphere is given by the formula V = (4/3)πR3, where R is the radius of the sphere. To find the radius, we set the two volume expressions equal to each other and solve for R.

Substituting the value for V, we get
40 = (4/3)πR3
Now, solve for R:
R = ∓((3 × 40) / (4π))
Simplifying yields an answer for R, and when calculated it is approximately 2.04 cm.