Cross Sections and Geometric Modeling Test Answer Key with Scoring – Geometry

Question 1 Name the Cross Sections (2 points)

(a) a circle, smaller than the base. (b) a rectangle.

(a) circle (b) rectangle

Scoring: 1 point each.

Question 2 Slice of a Cone (2 points)

The scale factor is 1220 = 35. Radius = 12 · 35 = 7.2 in.

Area = π(7.2²) = 51.84π ≈ 162.9 in².

7.2 in; 51.84π ≈ 162.9 in²

Scoring: 1 point each.

Question 3 Rotated Triangle (2 points)

Cone with radius 7 and height 9. V = 13π(7²)(9) = 147π ≈ 461.81.

Cone; ≈ 461.8 cubic units

Scoring: 1 point for the solid, 1 point for the volume.

Question 4 Compare Densities (3 points)

A: 28,350 ÷ 63 = 450. B: 120,900 ÷ 190 ≈ 636.32.

636.3 is greater than 450.

A: 450 per mi²; B: ≈ 636.3 per mi²; County B is denser

Scoring: 1 point for each density, 1 point for the comparison.

Question 5 Furnace Choice (3 points)

Volume = 20 · 15 · 9 = 2,700 ft³. BTUs needed = 2,700 · 24 = 64,800.

Furnace A (60,000) is too small. Furnace B (75,000) is enough.

64,800 BTUs; only furnace B

Scoring: 1 point for the volume, 1 point for the BTUs, 1 point for the decision.

Question 6 Design a Container (3 points)

π(5²)h = 1,000, so h = 100025π = 40π ≈ 12.73.

12.7 is greater than 12, so it does not fit.

h ≈ 12.7 cm; does not fit

Scoring: 1 point for the equation, 1 point for the height, 1 point for the decision.

Question 7 Grain Bin (3 points)

Volume = π(8²)(20) = 1,280π ≈ 4021.24 ft³.

Bushels = 4021.24 ÷ 1.244 ≈ 3232.51.

≈ 3233 bushels

Scoring: 1 point for the volume, 1 point for the conversion, 1 point for the answer.

Question 8 Rotate the Shape (2 points)

(a) a cylinder. (b) a sphere.

(a) cylinder (b) sphere

Scoring: 1 point each.