Volume of Spheres and Hemispheres
Written by Adi Ackerman, Head Teacher
"Volume of Spheres and Hemispheres" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.G.C.9. A 7th grader who is already steady on geometry can use it too, and an older student can use it as a short review.
8th grade math worksheet: find sphere and hemisphere volumes in terms of pi, using two thirds pi r cubed for each half sphere. Answer key included. Part of our volume of cylinders, cones and spheres geometry collection. Aligned to Common Core standards.
How do I use this worksheet?
Hand out the formula reference first, then move from cylinders to cones to spheres. Use the mixed and missing dimension sheets for review before a test.
What students will practice
- Students will find sphere volumes with V = ⁴⁄₃πr³ and leave answers in terms of π.
- Students will find hemisphere volumes with V = ⅔πr³ as half of a sphere.
- Students will find the radius from a diameter such as 12 in or 18 m first.
Name Angle Pairs Formed by a Transversal
Find Angles on Parallel Lines Cut by a Transversal
Solve for x With Transversal Angle Pairs
Triangle Angle Sum, Find the Missing Angle
Why Triangle Angles Sum to 180 Degrees
Quadrilateral Angle Sums From Two Triangles
Triangle Interior Angles, Solve for the Variable
Exterior Angle of a Triangle, Find the Measure
Curriculum Links
Common Core State Standards
Geometry · 8th Grade
Standard: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
View all 8.G.C.9 worksheets →Find this in the curriculum
Browse the grade, subject, and topic this belongs to.
FAQ
How do I use this volume of cylinders, cones and spheres worksheet?
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Hand out the formula reference first, then move from cylinders to cones to spheres. Use the mixed and missing dimension sheets for review before a test.
What does this worksheet teach?
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Find sphere and hemisphere volumes in terms of pi, using two thirds pi r cubed for each half sphere. The directions on the page read: Sphere: V = 4 3 πr³. A hemisphere is half of a sphere, so V = 2 3 πr³. If the diameter d is given, find r first. An answer key is included.
Can I use this volume of cylinders, cones and spheres worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade geometry, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
What is the formula for the volume of a cone?
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V = ⅓πr²h, one third of the volume of a cylinder with the same base and height. A cone with r = 3 in and h = 5 in has a volume of about 47.1 in³. Volume of Cones, Radius and Height Given has eight cones to practice.
How do you find the volume of a sphere?
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Cube the radius, multiply by π and then by 4/3. If you are given the diameter, halve it first. Volume of Spheres From the Radius mixes radius and diameter problems.
How do you find a missing height from a cylinder's volume?
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Substitute the volume and the radius into V = πr²h and solve for h. With r = 3 cm and V = 72π cm³, 9πh = 72π, so h = 8 cm. Find a Missing Dimension From the Volume practices this.
What is a composite solid?
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It is a solid made of simpler parts, such as a cylinder with a cone on top. Find each part's volume and add them. Volume of Composite Solids With Curves has four such solids.
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Name Angle Pairs Formed by a Transversal
Find Angles on Parallel Lines Cut by a Transversal
Solve for x With Transversal Angle Pairs
Triangle Angle Sum, Find the Missing Angle
Why Triangle Angles Sum to 180 Degrees
Quadrilateral Angle Sums From Two Triangles
Triangle Interior Angles, Solve for the Variable
Exterior Angle of a Triangle, Find the Measure