How many cubic units are in the volume of a cylinder whose height is four units and whose radius is five units?
What is the surface area of a cube whose volume is 27 cubic inches?
Volume of a cylinder = area of the base * height, or:
V = pi*(r^2)*h
therefore,
V = pi*(5^2)*4
V = pi*25*4
simplify this. units is in cubic units.
Volume of cube is s^3,, solving for the length of one side:
V = 27 = s^3
cuberoot(27) = s
s = 3 inches
Surface area of cube = 6*area of each face, or:
SA = 6*(s^2)
therefore,
SA = 6*(3^2)
simplify this. units is in square inches.
hope this helps. :)
How many cubic centimeters can a cigar box hold if its dimensions are 4 centimeters by 14 centimeters by 12 centimeters? Include correct units with your solution.
To find the volume of a cylinder, we use the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
1. Given that the height of the cylinder is 4 units and the radius is 5 units, we can substitute these values into the formula.
V = π(5^2)(4)
V = π(25)(4)
V = 100π
Therefore, the volume of the cylinder is 100π cubic units.
To find the surface area of a cube, we use the formula A = 6s^2, where A is the surface area and s is the length of the side of the cube.
2. Given that the volume of the cube is 27 cubic inches, we need to find the length of each side.
To do this, we can find the cube root of 27.
∛27 = 3
Therefore, the length of each side of the cube is 3 inches.
Now, we can substitute this value into the surface area formula.
A = 6(3^2)
A = 6(9)
A = 54 square inches
Therefore, the surface area of the cube is 54 square inches.
To find the volume of a cylinder, you can use the formula V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius, and h is the height.
For the first question, the height of the cylinder is given as four units, and the radius is given as five units.
Substituting these values into the formula, we get V = 3.14 * 5^2 * 4. Simplifying this, we have V = 3.14 * 25 * 4, which is equal to 314 cubic units.
Therefore, the volume of the cylinder is 314 cubic units.
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To find the surface area of a cube, you can use the formula SA = 6s^2, where SA is the surface area and s is the length of a side of the cube.
For the second question, the volume of the cube is given as 27 cubic inches. Since a cube has all sides equal in length, we can find s using the formula for the volume of a cube V = s^3.
We have 27 = s^3. Taking the cube root of both sides, we find s = 3.
Now that we know s, we can find the surface area of the cube using the formula SA = 6s^2. Substituting s = 3, we get SA = 6 * 3^2, which is equal to 54 square inches.
Therefore, the surface area of the cube is 54 square inches.