8th Grade Volume of Cylinders, Cones and Spheres Test Solutions and Scoring (PDF)

8th Grade math test solutions: Volume of Cylinders, Cones and Spheres – Maths PDF

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This volume cylinders cones spheres test answers for 8th Grade covers volume of cylinders, cones and spheres (Common Core 8.G.C.9), with a free PDF to print.

Use this answer key to score the volume of cylinders, cones and spheres test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.G.C.9

Volume cylinders cones spheres test answers: worked solutions

Question 1 – Cylinder [3 pts]

V = 144π m³.

\(V = \pi \cdot 16 \cdot 9 = 144\pi\). \(144 \cdot 3.14 = 452.16 \approx 452.2\).

Scoring: 1 point for the setup, 1 point for \(144\pi\), 1 point for 452.2.

Question 2 – Cone [3 pts]

V = 75π in³.

\(V = \frac{1}{3}\pi \cdot 25 \cdot 9 = 75\pi\).

Scoring: 1 point for the formula, 1 point for the substitution, 1 point for \(75\pi\) cubic inches.

Question 3 – Sphere [3 pts]

Radius 5: \(V = \frac{4}{3}\pi \cdot 125 = \frac{500}{3}\pi\).

Scoring: 1 point for the radius, 1 point for the formula, 1 point for \(\frac{500}{3}\pi\).

Question 4 – Find a dimension [3 pts]

\(200\pi = \pi r^{2} \cdot 8\), so \(r^{2} = 25\) and \(r = 5\) feet.

Scoring: 1 point for the equation, 1 point for \(r^{2} = 25\), 1 point for 5 ft.

Question 5 – Compare [2 pts]

The cone holds one third as much: \(30\pi\).

Scoring: 1 point for \(30\pi\). 1 point for the explanation.

Question 6 – Combined solid [3 pts]

Cylinder: \(\pi \cdot 9 \cdot 10 = 90\pi\). Hemisphere: \(\frac{2}{3}\pi \cdot 27 = 18\pi\).

Total: \(108\pi\) cubic centimeters.

Scoring: 1 point for each part, 1 point for the total.

Question 7 – Real world [2 pts]

Radius 5. \(V = 3.14 \cdot 25 \cdot 2 = 157\).

Scoring: 1 point for the radius. 1 point for 157 cubic inches.

Question 8 – Explain [1 pt]

The radius is cubed in the formula, and \(2^{3} = 8\).

Scoring: Full credit for mentioning the cube of the radius.

Total score

Total

20 points

Key facts behind this volume cylinders cones spheres test answers

Key facts

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 test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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