Answer:
1577.20 ft³
Step-by-step explanation:
Cube of length = 12 ft = a
Hole diameter which is cutout = 4 ft = d
Hole radius which is cutout = 4/2 =2 ft = r
Volume of the cube = a³
⇒Volume of the cube = a×a×a
⇒Volume of the cube = 12×12×12
⇒Volume of the cube = 1728 ft³
The hole cut out will be in the shape of a cylinder
Volume of cylinder = πr²h
⇒Volume of cylinder = π×2²×12
⇒Volume of cylinder = 150.79 ft³
Now volume of the solid figure with hole cut out is
Volume of the cube - Volume of cylinder
=1728 - 150.79
=1577.20 ft³
∴ Volume of solid figure not including hole cutout is 1577.20 ft³
Answer:
Conservation of energy, principle of physics according to which the energy of interacting bodies or particles in a closed system remains constant. ... For example, when a pendulum swings upward, kinetic energy is converted to potential energy.
Step-by-step explanation:
Answer:
y" = -24 / y³
Step-by-step explanation:
6x² + y² = 4
Take the derivative of both sides with respect to x.
12x + 2y y' = 0
Again, take the derivative of both sides with respect to x.
12 + 2y y" + y' (2y') = 0
12 + 2y y" + 2(y')² = 0
Solve for y' in the first equation.
2y y' = -12x
y' = -6x/y
Substitute and solve for y":
12 + 2y y" + 2(-6x/y)² = 0
12 + 2y y" + 2(36x²/y²) = 0
12 + 2y y" + 72x²/y² = 0
6y² + y³ y" + 36x² = 0
y³ y" = -36x² − 6y²
y" = (-36x² − 6y²) / y³
Solve for y² in the original equation and substitute:
y² = 4 − 6x²
y" = (-36x² − 6(4 − 6x²)) / y³
y" = (-36x² − 24 + 36x²) / y³
y" = -24 / y³
Answer:
Volume of a cone 
Step-by-step explanation:
Given that the radius of a cone is 15cm and its height is 4cm
That is r=15cm and h=4cm
To find the volume of a cone :
volume of a cone
cubic units
Now substitute the values in the formula we get
volume of a cone
Now round to nearest hundredth
Therefore Volume of a cone
