(a) v = πr^2 h = 1400π cm^3
(b) 216 = 6^3, so ...
and volume is in cm^3, not cm^2
(b) 216 = 6^3, so ...
and volume is in cm^3, not cm^2
Volume = π * radius^2 * height
Given that the diameter is 20 cm, we can calculate the radius by dividing it by 2:
Radius = 20 cm / 2 = 10 cm
Plugging in the values, we have:
Volume = π * (10 cm)^2 * 14 cm
Volume = 3.14 * 100 cm^2 * 14 cm
Volume = 4396 cm^3
Therefore, the volume of the cylindrical tin is 4396 cm^3.
(b) To find the edge of a cube with a volume of 216 cm^3, we need to find the cube root of the volume.
Cube root of 216 cm^3 = ∛216 cm^3
Using a calculator, we find:
∛216 = 6
Therefore, the edge of the cube is 6 cm.
In this case, we are given the diameter of the tin, which is 20 cm. To find the radius, we need to divide the diameter by 2: r = 20 cm / 2 = 10 cm.
The depth of the tin is given as 14 cm.
Now, we can substitute these values into the formula:
V = π (10 cm)^2 (14 cm)
V = 3.14 * 100 cm^2 * 14 cm
V = 3.14 * 1400 cm^3
V ≈ 4396 cm^3
So, the volume of the tin is approximately 4396 cm^3.
Moving on to the second part of your question, to find the edge length of a cube with a given volume, we need to find the cube root of the volume.
In this case, the volume of the cube is given as 216 cm^3. To find the edge length, we need to find the cube root of 216: ∛216 ≈ 6 cm.
So, the edge length of a cube with a volume of 216 cm^3 is approximately 6 cm.