GED Mathematical Reasoning Geometry and Measurement 4

Question 1

A right circular cone has a slant height of 13 cm and a base radius of 5 cm. What is the total surface area of the cone?

Accepted Answer

90π cm²

Answer

Total surface area of a cone = πr² + πrl, where r is the base radius and l is the slant height. = π(5)² + π(5)(13) = 25π + 65π = 90π cm².

Question 2

Two similar triangles have areas of 36 cm² and 100 cm². If the perimeter of the smaller triangle is 24 cm, what is the perimeter of the larger triangle?

Accepted Answer

40 cm

Answer

The ratio of areas of similar figures equals the square of the ratio of corresponding lengths. Area ratio = 36/100 = 9/25, so the side-length ratio = √(9/25) = 3/5. Perimeter of larger triangle = 24 × (5/3) = 40 cm.

Question 3

A rectangular prism has a length of 8 m, a width of 5 m, and a height of 3 m. If all three dimensions are doubled, by what factor does the volume increase?

Accepted Answer

8

Answer

Original volume = 8 × 5 × 3 = 120 m³. New volume = 16 × 10 × 6 = 960 m³. Factor = 960 ÷ 120 = 8. When all three linear dimensions are doubled, volume increases by 2³ = 8.

Question 4

Point A is located at (−3, 4) and point B is located at (5, −2) on a coordinate plane. What is the midpoint of segment AB, and what is the length of AB?

Accepted Answer

Midpoint (1, 1); Length 10

Answer

Midpoint = ((−3+5)/2, (4+(−2))/2) = (2/2, 2/2) = (1, 1). Length = √[(5−(−3))² + (−2−4)²] = √[8² + (−6)²] = √[64 + 36] = √100 = 10.

Question 5

A circular swimming pool has a diameter of 14 feet. A square deck is built around the outside of the pool, with each side of the square equal to the diameter of the pool. What is the area of the deck only (the part NOT covered by the pool)?

Accepted Answer

196 − 49π ft²

Answer

Area of square = 14² = 196 ft². Area of circular pool = π × r² = π × 7² = 49π ft². Deck area = 196 − 49π ≈ 196 − 153.94 ≈ 42.06 ft².

GED Practice Test

GED Practice Test

GED Mathematical Reasoning Geometry and Measurement 4