TMUA Geometry & Measurement Concepts 3

Question 1

An arc of a circle subtends an angle of 2 radians at the center. If the arc length is 8 cm, what is the area of the sector?

Accepted Answer

16 cm²

Answer

Arc length s = rθ → r = 4 cm; sector area = ½r²θ = ½·16·2 = 16 cm².

Question 2

A regular hexagon has side length 4 cm. What is its area?

Accepted Answer

24√3 cm²

Answer

Area of regular hexagon = (3√3/2)s² = (3√3/2)·16 = 24√3 cm².

Question 3

Two parallel lines are cut by a transversal. One co-interior angle is 3x + 10° and the other is 2x + 20°. Find x.

Accepted Answer

30°

Answer

Co-interior (same-side interior) angles sum to 180°: 5x + 30 = 180 → x = 30°.

Question 4

A cone has base radius 3 cm and slant height 5 cm. What is its total surface area?

Accepted Answer

24π cm²

Answer

Total surface area = πrl + πr² = π·3·5 + π·9 = 15π + 9π = 24π cm².

Question 5

In a circle, a chord of length 16 cm is 6 cm from the center. What is the radius?

Accepted Answer

10 cm

Answer

The perpendicular from center bisects the chord; r = √(8²+6²) = √100 = 10 cm.

(TMUA) Test of Mathematics for University Admission Practice Test