Since V = (4/3) * pi * R^3
If R is halved, V' will reduce by a ratio of (1/2)^3 = 1/8
So V' = (1/8)V
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
(c+8)(c-8)
3(2y+5)(2y-5)
There are no like terms so it's still ab^2-b
Answer:
v ≈ 8.5 km/h
Step-by-step explanation:
Since the diameter of the wheel is 3 m the radius will be r = 1.5 m.
Use the radius of the water wheel to find it's circumference C:
[set r = 1.5 m]
⇒ 
⇒ 
m
One revolution of the water wheel corresponds to 
meters so the angular velocity 15 rmp (revolutions per minute) corresponds to:
= 
/min
Using this result, the speed of the river in kilometers per hour will be:
× 
× 
⇒ 
⇒ 
≈ 
km/h
