Question

Find the capacity of a hemespherical bowl if the circumferece of the edge is 94.2cm

Answer 1

Answer:

7057.8 cm³  (approx)

Step-by-step explanation:

For the circles that is the edge:

circumference = 2 π r

=> r = circumference / 2π = 94.2 / 2π  = 47.1 / π

As the bowl is a hemisphere, the centre of the circle that is the edge is the centre of the sphere.  So the radius we have calculated above is the radius of the sphere that the bowl is half of.

Volume of sphere = (4/3) π r³

so

Volume of bowl = Half volume of sphere

= (2/3) π r³

= (2/3) × π × ( 47.1 / π )³

= (2/3) × (47.1)³ / π²

≈ 7057.8 cm³

[ Notice the importance of avoiding round-off errors by not approximating intermediate values.  If we round-off the value for r we would use r=15.0, which leads to a volume of 7068.6, and that is out by 10.8 cm³!!]