The volume Vr (in cubic meters) of a spherical balloon with radius r meters is given by =Vr43πr3.The radius Wt (in meters) after t seconds is given by =Wt+4t3.Write a formula for the volume Mt (in cubic meters) of the balloon after t seconds.It is not necessary to simplify.
Question
The volume Vr (in cubic meters) of a spherical balloon with radius r meters is given by =Vr43πr3.The radius Wt (in meters) after t seconds is given by =Wt+4t3.Write a formula for the volume Mt (in cubic meters) of the balloon after t seconds.It is not necessary to simplify.
Solution 1
The volume Mt of the balloon after t seconds can be found by substituting the expression for Wt into the formula for Vr.
So, Mt = V(Wt) = 4/3π(Wt)^3 = 4/3π((t+4t^3)^3).
This is the formula for the volume Mt of the balloon after t seconds.
Solution 2
The volume Mt of the balloon after t seconds can be found by substituting the expression for Wt into the formula for Vr.
So, Mt = V(Wt) = 4/3 * π * (Wt)^3
But we know that Wt = r + 4t^3.
So, substituting Wt into the formula for Mt, we get:
Mt = 4/3 * π * (r + 4t^3)^3
This is the formula for the volume Mt of the balloon after t seconds.
Solution 3
The volume Mt of the balloon after t seconds can be found by substituting the expression for Wt into the formula for Vr.
So, Mt = V(Wt) = 4/3 * π * (Wt)^3
But we know that Wt = r + 4t^3.
So, substituting Wt into the formula for Mt, we get:
Mt = 4/3 * π * (r + 4t^3)^3
This is the formula for the volume Mt of the balloon after t seconds.
Similar Questions
The surface area Sr (in square meters) of a spherical balloon with radius r meters is given by =Sr4πr2.The radius Pt (in meters) after t seconds is given by =Pt53t.Write a formula for the surface area Nt (in square meters) of the balloon after t seconds.It is not necessary to simplify.
A spherical balloon with radius r inches has volume V(r) = 43𝜋r3. Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 2 inches. (Express your answer in terms of 𝜋 and r.)
A spherical balloon is filled with air at the constant rate of 200cm2s.Calculate the rate at which the radius is increasing when the radius is10cm.1
A spherical balloon is released from rest and expands as it rises. After rising for t seconds, its radius is r cm, and its surface area is A cm2, where A = 4r2. The initial radius of the balloon is 16 cm. Given that the rate of increase of the radius is constant and has the value of 0.8 cm s– 1, find the rate of increase of A when t = 5.
A meteorological balloon rises through the atmosphere until it expands to a volume of 1.0 × 10 6 m 3, wherethe pressure is 1.0 × 10 3 Pa. The temperature also falls from 17 °C to − 43 °C.The pressure of the atmosphere at the Earth’s surface = 1.0 × 10 5 Pa.Show that the volume of the balloon at take off is about 1.3 × 10 4 m 3
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.