Mathematics
Grade 10
15 min
Surface area and volume of spheres
Surface area and volume of spheres
What you'll learn
- Identify and name all four quadrants (I, II, III, and IV) on a coordinate plane with 100% accuracy.
- Explain the characteristics of each quadrant (positive/negative x and y values) using complete sentences for each quadrant.
- Plot and accurately identify the quadrant of at least 8 out of 10 given points on a coordinate plane.
- Apply knowledge of quadrants to describe the location of real-world objects on a simple map represented as a coordinate plane, using quadrant numbers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a sphere and its key components (radius, diameter, great circle, hemisphere).
Recall and correctly apply the formulas for the surface area and volume of a sphere.
Calculate the surface area and volume of a sphere given its radius or diameter.
Calculate the surface area (curved and total) and volume of a hemisphere.
Solve for the radius or diameter of a sphere when given its surface area or volume.
Apply the sphere formulas to solve real-world and multi-step problems.
Have you ever wondered how much air is inside a basketball or how much leather is needed to cover it? 🏀 That's exactly what we'll learn to calculate today!
This tutorial will guide you through the formulas for calculating the surface area (the 'skin') and volume (...
2
Key Concepts & Vocabulary
TermDefinitionExample
SphereA perfectly round three-dimensional geometric object. It is the set of all points in space that are equidistant from a fixed point called the center.A basketball, a marble, or a planet like Earth (approximated as a sphere).
Radius (r)The distance from the center of the sphere to any point on its surface.If a gumball's center is 1 cm away from its surface, its radius is 1 cm.
Diameter (d)A straight line segment that passes through the center of the sphere and whose endpoints lie on the sphere. It is always twice the length of the radius (d = 2r).If a sphere has a radius of 5 meters, its diameter is 10 meters.
Great CircleThe largest possible circle that can be drawn on the surface of a sphere. Its plane passes through the center of the sphere.The Earth'...
3
Core Formulas
Surface Area of a Sphere
SA = 4 * \pi * r^2
Use this formula to find the total area of the outer surface of a sphere. It's equivalent to the area of four circles with the same radius as the sphere. Remember to use the radius (r), not the diameter.
Volume of a Sphere
V = (4/3) * \pi * r^3
Use this formula to find the amount of space inside a sphere. Notice the radius is cubed (r^3), which is a key feature of volume calculations for 3D figures.
Total Surface Area of a Hemisphere
SA = 3 * \pi * r^2
Use this to find the total surface area of half a sphere, which includes the curved surface (2 * \pi * r^2) and the flat circular base (\pi * r^2).
Volume of a Hemisphere
V = (2/3) * \pi * r^3
Use this to find the volume of half a sphere. It is exactly half the v...
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Challenging
A large spherical metal ball with a radius of 6 cm is melted down and recast into smaller spherical bearings, each with a radius of 2 cm. Assuming no material is lost, how many small bearings can be made?
A.3
B.9
C.18
D.27
Challenging
For a specific sphere, the numerical value of its surface area in square units is equal to the numerical value of its volume in cubic units. What is the diameter of this sphere?
A.3 units
B.4/3 units
C.6 units
D.4 units
Challenging
A sphere is perfectly inscribed in a cylinder (it touches the top, bottom, and sides). What is the ratio of the volume of the sphere to the volume of the cylinder?
A.1/2
B.3/4
C.2/3
D.1/3
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Frequently asked questions
What grade level is "Surface area and volume of spheres"?
Surface area and volume of spheres is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Surface area and volume of spheres?
You'll be able to: Identify and name all four quadrants (I, II, III, and IV) on a coordinate plane with 100% accuracy; Explain the characteristics of each quadrant (positive/negative x and y values) using complete sentences for each quadrant; Plot….
Is "Surface area and volume of spheres" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Surface area and volume of spheres?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.