oobleck
answered
Or, you can use the handy formula V = πh/3 (R^2+rR+r^2)
v = 1/3 π*4(12^2 + 12*8 + 8^2)
R_scott
answered
if the sides were extended downward
... the entire cone would be 12 cm deep ... 4 cm / [1 - (8 cm / 12 cm)]
the volume of the entire cone would be ... 1/3 * π * (6 cm)^2 * 12
the volume of the extension would be ... 1/3 * π * (4 cm)^2 * 8
the volume of the bucket is the difference ... entire minus extension
Step-by-Step Bot
answered
V = (π * h/3) * (R^2 + r^2 + R*r)
where:
V = Volume
π = Pi (approximately 3.14159)
h = Height of the frustum
r = Radius of the smaller circular base
R = Radius of the larger circular base
In this case, the height of the frustum (bucket depth) is given as 4 cm, the radius of the smaller circular base (bottom diameter/2) is 8/2 = 4 cm, and the radius of the larger circular base (top diameter/2) is 12/2 = 6 cm.
Substituting these values into the formula:
V = (π * 4/3) * (6^2 + 4^2 + 6*4)
Simplifying:
V = (π * 4/3) * (36 + 16 + 24)
V = (π * 4/3) * 76
V ≈ 3.14159 * 4/3 *76
V ≈ 4.188 * 76
V ≈ 322.048 cubic centimeters
Therefore, the volume of the bucket is approximately 322.048 cubic centimeters.
Explain Bot
answered
To get the volume of a frustum, you can use the following formula:
Volume = (1/3) * π * h * (r₁² + r₂² + r₁*r₂)
Here,
- h is the height of the frustum (depth of the bucket)
- r₁ is the radius of the top of the frustum (diameter at the top divided by 2)
- r₂ is the radius of the bottom of the frustum (diameter at the bottom divided by 2)
- π is a mathematical constant approximately equal to 3.14159
In this case,
- h = 4cm
- r₁ = (12cm / 2) = 6cm
- r₂ = (8cm / 2) = 4cm
Now, using the formula, we can calculate the volume of the bucket:
Volume = (1/3) * π * 4cm * (6² + 4² + 6cm * 4cm)
= (1/3) * π * 4cm * (36cm² + 16cm² + 24cm²)
= (1/3) * π * 4cm * 76cm²
= (4/3) * π * 4cm * 76cm²
= (16/3) * 76π cm³
≈ 804 cm³ (approximately)
Therefore, the volume of the bucket is approximately 804 cm³.
