DSAT DSAT Geometry and Trigonometry 3

Question 1

A cone has a radius of 3 and a height of 4. What is the volume of the cone?

Accepted Answer

12π

Answer

Volume of a cone = (1/3)πr²h = (1/3) × π × 9 × 4 = 12π.

Question 2

Two similar triangles have corresponding sides in a ratio of 3:5. If the area of the smaller triangle is 27, what is the area of the larger triangle?

Accepted Answer

75

Answer

The ratio of areas of similar figures equals the square of the ratio of corresponding sides: (3/5)² = 9/25, so area = 27 × (25/9) = 75.

Question 3

In the coordinate plane, what is the distance between points (1, 2) and (5, 5)?

Accepted Answer

5

Answer

Distance = √[(5−1)² + (5−2)²] = √[16 + 9] = √25 = 5.

Question 4

An arc of a circle subtends a central angle of 60° and has a radius of 6. What is the arc length?

Accepted Answer

2π

Answer

Arc length = (θ/360) × 2πr = (60/360) × 2π(6) = (1/6) × 12π = 2π.

Question 5

If the surface area of a cube is 96 square units, what is the length of one side?

Accepted Answer

4

Answer

Surface area of a cube = 6s², so 96 = 6s², s² = 16, s = 4.

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