Geometry

Written by Hassan Raza (Mathematics)

SAT for LUMS · ریاضی · 17 سوالات

نام: ____________________ تاریخ: ____________

The legs of a right triangle are 6 and 8. What is the length of the hypotenuse?
- A 12
- B 7
- C 10
- D 14
What is the circumference of a circle with radius 5?
- A 10π
- B 5π
- C 20π
- D 25π
What is the area of a circle with radius 3?
- A 18π
- B 9π
- C 6π
- D 3π
Two angles of a triangle are 50° and 60°. What is the third angle?
- A 70°
- B 60°
- C 110°
- D 80°
A rectangle is 9 units long and 4 units wide. What is its area?
- A 13
- B 36
- C 18
- D 26
Two angles of a triangle are 90° and 35°. What is the third angle?
- A 65°
- B 55°
- C 125°
- D 45°
What is the volume of a cube with side 3?
- A 27
- B 18
- C 9
- D 12
What is the area of a circle with diameter 10?
- A 10π
- B 5π
- C 25π
- D 100π
In a right triangle the hypotenuse is 13 and one leg is 5. What is the other leg?
- A 12
- B 18
- C 9
- D 8
In a right triangle with sides 3, 4 and 5, what is sin A, if the side opposite angle A is 3?
- A 3/4
- B 4/5
- C 5/3
- D 3/5
The area of a circle is 49π. What is its circumference?
- A 14π
- B 49π
- C 7π
- D 98π
The legs of a right triangle are 7 and 24. What is the length of the hypotenuse?
- A 17
- B 31
- C 25
- D 26
Two parallel lines are cut by a transversal. One of the co-interior angles is 70°. What is the other?
- A 20°
- B 70°
- C 110°
- D 90°
What is the volume of a cylinder of radius 2 and height 5?
- A 25π
- B 40π
- C 10π
- D 20π
In a 45°, 45°, 90° triangle each leg is 6. What is the length of the hypotenuse?
- A 6√2
- B 3√2
- C 6√3
- D 12
Two similar triangles have sides in the ratio 1 : 3. The smaller triangle has an area of 4. What is the area of the larger triangle?
- A 16
- B 12
- C 24
- D 36
If sin 20° = cos x°, what is the value of x?
- A 80
- B 70
- C 40
- D 20

جوابی کلید

1. C, 2. A, 3. B, 4. A, 5. B, 6. B, 7. A, 8. C, 9. A, 10. D, 11. A, 12. C, 13. C, 14. D, 15. A, 16. D, 17. B

By the Pythagorean theorem, the hypotenuse is √(36 + 64) = 10.
Circumference = 2πr = 10π.
Area = πr² = 9π.
The angles of a triangle add up to 180°, and 180 − 110 = 70.
Area = 9 × 4 = 36.
The angles add up to 180°.
Volume = 3³ = 27.
The radius is 5, so the area is π × 25.
The leg is √(169 − 25) = 12.
Sine is the opposite side divided by the hypotenuse.
The radius is 7, so the circumference is 2π × 7.
The hypotenuse is √(49 + 576) = 25.
Co-interior angles add up to 180°.
Volume = πr²h = π × 4 × 5.
The hypotenuse is the leg times √2.
The areas are in the ratio 1 : 9.
The sine of an angle equals the cosine of its complement.