How fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
To solve the question, we need to know the volume of a sphere
<h3>
Volume of a sphere</h3>
The volume of a sphere V = 4πr³/3 where r = radius of sphere.
<h3>How fast the volume of the sphere is changing</h3>
To find the how fast the volume of the sphere is changing, we find rate of change of volume of the sphere. Thus, we differentiate its volume with respect to time.
So, dV/dt = d(4πr³/3)/dt
= d(4πr³/3)/dr × dr/dt
= 4πr²dr/dt where
- dr/dt = rate of change of radius of sphere and
- 4πr² = surface area of sphere
Given that
- dr/dt = + 3 cm/s (positive since it is increasing) and
- 4πr² = surface area of sphere = 10 cm²,
Substituting the values of the variables into the equation, we have
dV/dt = 4πr²dr/dt
dV/dt = 10 cm² × 3 cm/s
dV/dt = 30 cm³/s
So, how fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
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<span>I'm pretty sure that the following polynomial 23 + 4x3 is a cubic binomial.</span>
Answer:
3y + 2
Step-by-step explanation: add like terms
Answer:
Step-by-step explanation:
1. Proportion.
= 
2.Lets cross multiply.
3.Solve
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Hope this helps :)
The area of that rectangle is 150 square inches. The result is obtained by using the formula of the perimeter dan area of pictures.
<h3>How to find the perimeter and area of a rectangle?</h3>
A rectangle is a two dimensional shape consisting of four joints. It has also four angle points.
The perimeter and area of a rectangle can be expressed as follows.
P = 2 (w + l)
A = w × l
Where
- P = perimeter of a rectangle
- A = area of a rectangle
- w = width of a rectangle
- l = length of a rectangle
The perimeter of a rectangle is 800 inches. The width of the rectangle is 60% of its length.
From that information, we have:
- P = 800 inches
- w = 60% × l = 0.6l
P = 2(w + l)
800 = 2(0.6l + l)
400 = 1.6l
l = 400/1.6
l = 250 inches
The area of the rectangle is
A = w × l
A = 0.6 l × l
A = 0.6 l²
A = 0.6 × 250
A = 150 square inches
Hence, the area of that rectangle is 150 square inches.
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