Question

a container for a hanging plant is a half sphere with a diameter of 9 inches. about how much soil does the container hold

Answer 1

190.87 cubic inches

Explanation:

A sphere is three-dimensional a ball-shaped object. It's volume is calculated using the formula:

V = 4/3πr^3

Where V= Volume of sphere

π (pie) = 22/7 (constant)

r = diameter ÷ 2 i.e. 9/2 = 4.5inches

Hence, to calculate the volume of the sphere, we slot in the values into the formula;

V = 4/3 × 22/7 × 4.5^3

V = 1.333.....× 3.142 × 4.5 × 4.5 × 4.5

V = 381.753

Thus, the volume of the sphere is 381.753 cubic inches.

However, according to the question, the container is a hemisphere i.e. half of a sphere. Therefore, to get the volume of soil in the container, we divide the volume of the sphere by 2;

381.753 ÷ 2

= 190.87

Hence, the volume of the soil in the hemispherical container is 190.87 cubic inches (in^3)

Answer 2

190.9 in³

Explanation:

Whenever one is asked to find how much(quantity of something) a certain container can hold,all you need to understand is that you are been asked about the volume of that container

We all know that the volume of a sphere is 4/3 × 22/7 × r³

And since we are dealing with a container in the shape of half a sphere,the volume of that container will now be volume of a sphere divided by 2

If the formula that was given initially was divided by 2,the new formula will look like this:

4/6 × 22/7 × r³

And we have the diameter but not the radius and we know that to find the radius, all we need to do is to divide the diameter by 2

That is 9/2 = 4.5

Putting the values in the formula,we can now derive the volume of that sphere

4/6 × 22/7 × 4.5³

= 190.9 in³ of soil