Homework 10 volume and surface area of spheres and hemispheres – Homework 10 delves into the intriguing realm of spheres and hemispheres, where we explore their geometric characteristics. This journey begins with understanding the volume of spheres, delving into the formula that governs their three-dimensional space. As we progress, we uncover the formula for calculating the surface area of spheres, determining the extent of their external boundaries.
Our exploration continues with the volume of hemispheres, revealing the formula that defines their enclosed space. Finally, we unravel the formula for the surface area of hemispheres, uncovering the extent of their curved surfaces. Throughout this exploration, we will encounter captivating examples, illuminating tables, and thought-provoking questions that deepen our understanding of these fascinating geometric shapes.
Volume of Spheres
The volume of a sphere is the amount of three-dimensional space that it occupies. It is calculated using the formula:
V = (4/3)πr³
where:
- V is the volume of the sphere in cubic units
- π is a mathematical constant approximately equal to 3.14
- r is the radius of the sphere in units
For example, the volume of a sphere with a radius of 5 units is:
V = (4/3)π(5³) = (4/3)π(125) = 523.6 cubic units
Surface Area of Spheres: Homework 10 Volume And Surface Area Of Spheres And Hemispheres
The surface area of a sphere is the total area of its surface. It is calculated using the formula:
A = 4πr²
where:
- A is the surface area of the sphere in square units
- π is a mathematical constant approximately equal to 3.14
- r is the radius of the sphere in units
For example, the surface area of a sphere with a radius of 5 units is:
A = 4π(5²) = 4π(25) = 100π square units
Volume of Hemispheres
A hemisphere is half of a sphere. The volume of a hemisphere is calculated using the formula:
V = (2/3)πr³
where:
- V is the volume of the hemisphere in cubic units
- π is a mathematical constant approximately equal to 3.14
- r is the radius of the hemisphere in units
For example, the volume of a hemisphere with a radius of 5 units is:
V = (2/3)π(5³) = (2/3)π(125) = 261.8 cubic units
Surface Area of Hemispheres
The surface area of a hemisphere is the total area of its surface. It is calculated using the formula:
A = 3πr²
where:
- A is the surface area of the hemisphere in square units
- π is a mathematical constant approximately equal to 3.14
- r is the radius of the hemisphere in units
For example, the surface area of a hemisphere with a radius of 5 units is:
A = 3π(5²) = 3π(25) = 75π square units
FAQ Corner
What is the formula for calculating the volume of a sphere?
V = (4/3)πr³, where r is the radius of the sphere.
How do I calculate the surface area of a sphere?
A = 4πr², where r is the radius of the sphere.
What is the relationship between the radius and volume of a sphere?
The volume of a sphere is proportional to the cube of its radius (V ∝ r³).
How do I calculate the volume of a hemisphere?
V = (2/3)πr³, where r is the radius of the hemisphere.
What is the formula for the surface area of a hemisphere?
A = 3πr², where r is the radius of the hemisphere.
