Geometric and Spatial Reasoning Flashcards

A cone has a radius of 3 and a height of 8. What is its volume? (Use π ≈ 3.14)

Answer: 75.36

Volume of a cone = ⅓πr²h = ⅓ × 3.14 × 9 × 8 = 75.36.

Triangle ABC is similar to triangle DEF. If AB = 6, DE = 9, and BC = 8, what is EF?

Answer: 12

The scale factor is DE/AB = 9/6 = 1.5, so EF = BC × 1.5 = 8 × 1.5 = 12.

What is the sum of the interior angles of a pentagon?

Answer: 540°

The sum of interior angles of an n-sided polygon = (n − 2) × 180° = (5 − 2) × 180° = 540°.

Which transformation slides a figure to a new position without rotating or reflecting it?

Answer: Translation

A translation moves every point of a figure the same distance in the same direction.

What is the volume of a cylinder with radius 5 and height 10? (Use π ≈ 3.14)

Answer: 785

Volume of a cylinder = πr²h = 3.14 × 25 × 10 = 785.

What is the midpoint of a line segment with endpoints (2, 4) and (8, 10)?

Answer: (5, 7)

Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) = ((2+8)/2, (4+10)/2) = (5, 7).

A rectangle has a diagonal of length 13 and a width of 5. What is its length?

Answer: 12

Using the Pythagorean theorem: l² + 5² = 13², so l² = 169 − 25 = 144, and l = 12.