8th Grade Volume of Cylinders, Cones and Spheres Worksheet Solutions (PDF)
This volume cylinders cones spheres answers for 8th Grade covers volume of cylinders, cones and spheres (Common Core 8.G.C.9), with a free PDF to print.
This answer key gives a full worked solution for each of the 20 problems on the volume of cylinders, cones and spheres worksheet (Common Core 8.G.C.9). Compare each step with your own work, not only the final answer, and note any step where your method differed.
Grade 8 · Common Core State Standards: 8.G.C.9
Volume cylinders cones spheres answers: exercises 1 to 10
Exercise 1 – Cylinder volume
\(V = \pi \cdot 4^{2} \cdot 6 = 96\pi\).
\(96\pi \text{ ft}^{3}\)
Exercise 2 – Cylinder from a diameter
Radius \(= 5\). \(V = 3.14 \cdot 25 \cdot 7 = 549.5\).
549.5 cm³
Exercise 3 – Cone volume
\(V = \frac{1}{3}\pi \cdot 9 \cdot 7 = 21\pi\).
\(21\pi \text{ m}^{3}\)
Exercise 4 – Cone from a diameter
Radius \(= 4\). \(V = \frac{1}{3}\pi \cdot 16 \cdot 9 = 48\pi\).
\(48 \cdot 3.14 = 150.72\).
\(48\pi \approx 150.72 \text{ in}^{3}\)
Exercise 5 – Sphere volume
\(V = \frac{4}{3}\pi \cdot 9^{3} = \frac{4}{3}\pi \cdot 729 = 972\pi\).
\(972\pi \text{ in}^{3}\)
Exercise 6 – Sphere from a diameter
Radius \(= 6\). \(V = \frac{4}{3}\pi \cdot 216 = 288\pi\).
\(288 \cdot 3.14 = 904.32\).
\(288\pi \approx 904.32 \text{ in}^{3}\)
Exercise 7 – Find the height
\(150\pi = \pi \cdot 25 \cdot h\), so \(h = 6\).
6 cm
Exercise 8 – Find the cone height
\(100\pi = \frac{1}{3}\pi \cdot 25 \cdot h\), so \(300 = 25h\) and \(h = 12\).
12 inches
Exercise 9 – Find the radius of a sphere
\(\frac{4}{3}\pi r^{3} = \frac{256}{3}\pi\), so \(r^{3} = 64\).
4 units
Exercise 10 – Cylinder and cone
Cylinder: \(\pi \cdot 16 \cdot 9 = 144\pi\). Cone: \(\frac{1}{3} \cdot 144\pi = 48\pi\).
The cone is one third of the cylinder
Exercises 11 and up
Exercise 11 – Hemisphere
Half a sphere: \(\frac{1}{2} \cdot \frac{4}{3}\pi \cdot 216 = 144\pi\).
\(144\pi\)
Exercise 12 – Soup can
Radius \(= 3.5\). \(V = 3.14 \cdot 12.25 \cdot 4 = 153.86\).
about 153.9 in³
Exercise 13 – Water tank
\(V = \pi \cdot 16 \cdot 10 = 160\pi\).
\(160 \cdot 3.14 = 502.4\).
\(160\pi \approx 502.4 \text{ ft}^{3}\)
Exercise 14 – Ice cream
Cone: \(\frac{1}{3}\pi \cdot 4 \cdot 6 = 8\pi\).
Scoop: \(\frac{4}{3}\pi \cdot 8 = \frac{32}{3}\pi\).
Cone \(8\pi\) in³; scoop \(\frac{32}{3}\pi\) in³
Exercise 15 – Soccer ball
\(V = \frac{4}{3} \cdot 3.14 \cdot 4.5^{3} = \frac{4}{3} \cdot 3.14 \cdot 91.125 = 381.51\).
about 381.5 in³
Exercise 16 – Grain silo
Cylinder: \(\pi \cdot 25 \cdot 20 = 500\pi\). Hemisphere: \(\frac{2}{3}\pi \cdot 125 = \frac{250}{3}\pi\).
Total: \(500\pi + \frac{250}{3}\pi = \frac{1750}{3}\pi\).
\(\frac{1750}{3}\pi \approx 1831.7 \text{ ft}^{3}\)
Exercise 17 – Traffic cone
\(V = \frac{1}{3}\pi \cdot 36 \cdot 18 = 216\pi \approx 678.24\).
about 678.24 in³
Exercise 18 – Swimming pool
\(V = \pi \cdot 36 \cdot 4 = 144\pi \approx 452.16\).
about 452.2 ft³
Exercise 19 – Double the radius
Original: \(\pi \cdot 4 \cdot 5 = 20\pi\). New (\(r = 4\)): \(\pi \cdot 16 \cdot 5 = 80\pi\).
The volume is 4 times as large
Exercise 20 – Find the height with 3.14
\(502.4 = 3.14 \cdot 16 \cdot h = 50.24h\), so \(h = 10\).
10 feet
Key facts behind this volume cylinders cones spheres answers
- Cylinder: \(V = \pi r^{2} h\).
- Cone: \(V = \frac{1}{3}\pi r^{2} h\), one third of the matching cylinder.
- Sphere: \(V = \frac{4}{3}\pi r^{3}\); hemisphere: \(\frac{2}{3}\pi r^{3}\).
- Radius is half the diameter; cube or square the radius before multiplying.
- Doubling the radius multiplies cylinder volume by 4 and sphere volume by 8.
How to use this volume cylinders cones spheres answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
Download the volume cylinders cones spheres answers as a PDF with the button below and keep it with your notes.
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