TMUA Geometry & Measurement Concepts 2

Question 1

A sector of a circle has radius 6 cm and central angle 120°. What is the area of the sector?

Accepted Answer

12π cm²

Answer

Area of sector = (θ/360°)·πr² = (120/360)·π·36 = 12π cm².

Question 2

Two circles have radii in the ratio 3:5. What is the ratio of their areas?

Accepted Answer

9:25

Answer

Area scales with the square of radius, so the ratio is 3²:5² = 9:25.

Question 3

In triangle ABC, angle A = 90°, AB = 5, AC = 12. What is the length of the altitude from A to BC?

Accepted Answer

60/13

Answer

BC = 13 (Pythagorean theorem); altitude h = (AB·AC)/BC = 60/13.

Question 4

A cylinder has radius r and height 2r. If the radius is doubled and height halved, what happens to the volume?

Accepted Answer

It doubles

Answer

Original V = π r²·2r = 2πr³; new V = π(2r)²·r = 4πr³, which is twice the original.

Question 5

The diagonals of a rhombus are 10 cm and 24 cm. What is the perimeter of the rhombus?

Accepted Answer

52 cm

Answer

Each side = √(5²+12²) = 13 cm; perimeter = 4×13 = 52 cm.

(TMUA) Test of Mathematics for University Admission Practice Test