Volume of Cylinders Cones Spheres Test Answer Key with Scoring – Grade 8

Question 1 Cylinder volume (2 points)

V = π · 7² · 9 = π · 49 · 9.

441π ft³

Scoring: 1 point for the substitution, 1 point for the answer with units.

Question 2 Cone volume (2 points)

V = (1/3)π · 9² · 10 = (1/3)π · 810.

270π m³

Scoring: 1 point for the substitution, 1 point for the answer with units.

Question 3 Sphere volume (3 points)

(a) 15 ÷ 2 = 7.5 cm

(b) V = (4/3)π · 7.5³ = (4/3)π · 421.875 = 562.5π cm³

(c) 562.5 · 3.14 = 1,766.25 cm³

Scoring: 1 point per part.

Question 4 Water bottle (3 points)

(a) V = π · 4² · 20 = 320π cm³

(b) 320 · 3.14 = 1,004.8 cm³

(c) 1,004.8 ÷ 250 = 4.0192, so 4 full cups.

Scoring: 1 point per part.

Question 5 Missing height (3 points)

(a) 75π = (1/3)π · 5² · h = (25/3)πh, so h = 75 · 3 ÷ 25 = 9 in.

(b) π · 5² · 9 = 225π in³, which is 3 times 75π.

Scoring: part (a) 1 point for the equation, 1 point for the height; part (b) 1 point.

Question 6 Composite solid (3 points)

(a) π · 3² · 8 = 72π in³

(b) (1/3)π · 3² · 4 = 12π in³

(c) 72π + 12π = 84π, and 84 · 3.14 = 263.76 in³

Scoring: 1 point per part.

Question 7 Sphere and cylinder (2 points)

(a) Sphere: (4/3)π · 6³ = 288π in³. Cylinder: π · 6² · 12 = 432π in³.

(b) 288 ÷ 432 = 2/3

Scoring: 1 point per part.

Question 8 Gravel pile (2 points)

The radius is 5 ft. V = (1/3) · 3.14 · 5² · 6 = 3.14 · 50.

157 ft³

Scoring: 1 point for using the radius 5, 1 point for the volume.