Answer:
The exact value of its surface area = 144π m²
The exact value of its volume = 288π m³
Step-by-step explanation:
∵ The diameter of the sphere is 12m
∴ The radius of the sphere = 12 ÷ 2 = 6m
∵ The surface area of the sphere = 4πr²
∴ The surface area = 4 × π × 6² = 144π m²
∵ The volume of the sphere = 4/3 πr³
∴ The volume = = 288π m³
Answer:
The tip of the man shadow moves at the rate of
Step-by-step explanation:
Let's draw a figure that describes the given situation.
Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.
Here it forms two similar triangles.
Let's find the distance "y" using proportion.
From the figure, we can form a proportion.
Cross multiplying, we get
15(y -x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
y =
We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).
----(1)
We are given . Plug in the equation (1), we get
Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.
