A wooden stool is in the form of a frustum of a cone with slant edge 40cm,top diameter 30cm and bottom diameter 50cm.
a) calculate the perpendicular height of the stool
a wooden stool in the form of a frustrum a cone with a slant edge 40cm top diameter 30cm and bottom diameter 50cm calculate perpendicular height of stool
ans 30.8
Hae,where is the answer?
To calculate the perpendicular height of the stool, we need to use the formula for the volume of a frustum of a cone. The formula is:
V = (1/3)πh (r₁² + r₁r₂ + r₂²)
Where:
V = volume of the frustum
h = perpendicular height of the frustum
r₁ = radius of the top base (30cm in this case)
r₂ = radius of the bottom base (50cm in this case)
We know the volume of the frustum is zero because the stool is hollow, so we'll set V = 0 and solve for h. Let's plug in the given values:
0 = (1/3)πh (30² + 30(30/50) + (30/50)²)
Simplifying the equation:
0 = (1/3)πh (900 + 18 + 1.08)
0 = (1/3)πh (919.08)
Now, we can solve for h. Divide both sides of the equation by (1/3)π(919.08):
0 = h / (919.08/3.14)
0 = h / 292.68
To find the value of h, we need to divide both sides of the equation by 292.68:
h = 0 / 292.68
h = 0
Based on the calculations, the perpendicular height of the stool is 0 cm. However, it seems that there may have been an error or missing information in the given data.
since the radii differ by 10cm,
h^2 + 10^2 = 40^2