DSAT extra practice Ch5 Lv2

1. Question

According to a recipe, making an apple pie with 8-inch diameter and 1-inch height requires 300 ml of fresh cream. If Kyle wants to make an apple pie with 16-inch diameter and 1-inch height, how much fresh cream should he use?

600 ml
900 ml
1200 ml
2400 ml

2. Question

The figure shows a triangle [math]ABC[/math]. [math]D[/math] is on [math]\overline{BC}[/math]. If the area of triangle [math]ABD[/math] is 12, what is the area of triangle [math]ABC[/math]?

3. Question

The figure shows a playground of a school. If the perimeter of the playground is [math]a+b\pi[/math] meters, where [math]a[/math] and [math]b[/math] are integers, what is the value of [math]a+b[/math]?

[math]900[/math]
[math]1500[/math]
[math]1800[/math]
[math]2100[/math]

4. Question

In the figure, [math]ABCD[/math] is a rectangle and [math]CE=CD[/math]. If the perimeter of triangle [math]BED[/math] is equal to [math]a+\sqrt{b}+\sqrt{c}[/math] where [math]a, b[/math], and [math]c[/math] are positive integers, what is the value of [math]a+b+c[/math]?

[math]36[/math]
[math]38[/math]
[math]40[/math]
[math]42[/math]

5. Question

In the figure, [math]ABCD[/math] is a kite. [math]E[/math] is the intersection of [math]\overline{AC}[/math] and [math]\overline{BD}[/math]. If [math]AE=5, EC=7[/math] and [math]BD=6[/math], what is the perimeter of kite [math]ABCD[/math]?

[math]\sqrt{34}+\sqrt{58}[/math]
[math]2\sqrt{34}+2\sqrt{58}[/math]
[math]\sqrt{61}+\sqrt{85}[/math]
[math]2\sqrt{61}+2\sqrt{85}[/math]

6. Question

What is the length of [math]\overline{AD}[/math]?

7. Question

In the given figure, [math]ABCD-HEFG[/math] is a cuboid. If the area of triangle [math]ABH[/math] is equal to [math]a\sqrt{b}[/math] where [math]a[/math] and [math]b[/math] are both prime numbers, what is the value of [math]b[/math]?

[math]13[/math]
[math]41[/math]
[math]52[/math]
[math]61[/math]

8. Question

The figure shows a parallelogram [math]ABCD[/math]. If [math]m\angle ACB=(7x-2)^\circ[/math] and [math]m\angle CAD=(x^2+4)^\circ[/math], which of the following values could be [math]m\angle CAD[/math]?

[math]1^\circ[/math]
[math]5^\circ[/math]
[math]7^\circ[/math]
[math]12^\circ[/math]

9. Question

The figure shows an isosceles triangle [math]ABC[/math] where [math]AC=BC[/math]. If [math]m\angle C=40^\circ[/math], what is the measure of [math]\angle BAD[/math]?

[math]70^\circ[/math]
[math]50^\circ[/math]
[math]40^\circ[/math]
[math]20^\circ[/math]

10. Question

In the figure, [math]ABCD[/math] is a trapezoid and [math]ABED[/math] is a parallelogram. If [math]m\angle B=50^\circ[/math] and [math]m\angle C=70^\circ[/math], what is [math]m\angle CDE[/math]?

[math]50^\circ[/math]
[math]60^\circ[/math]
[math]70^\circ[/math]
[math]80^\circ[/math]

11. Question

In the figure, [math]ABC[/math] is an isosceles triangle and [math]BCD[/math] is an equilateral triangle. If [math]m\angle A=20^\circ[/math], what is the measure of [math]\angle ABD[/math]?

[math]10^\circ[/math]
[math]15^\circ[/math]
[math]20^\circ[/math]
[math]25^\circ[/math]

12. Question

Two triangles [math]ABC[/math] and [math]PQR[/math] are similar. If the area of [math]ABC[/math] is twice as large as the area of [math]PQR[/math], what is the value of [math]\dfrac{AB}{PQ}[/math]?

[math]2[/math]
[math]\sqrt{2}[/math]
[math]\dfrac{1}{2}[/math]
[math]\dfrac{1}{\sqrt{2}}[/math]

13. Question

In the figure, what is the length of [math]\overline{AB}[/math]?

14. Question

In the figure, triangles [math]ABC[/math] and [math]DCB[/math] are congruent. Which of the following statements about triangle [math]PBC[/math] must be true?

[math]PBC[/math] is a right triangle.
[math]PBC[/math] is an isosceles triangle.
[math]PBC[/math] is an equilateral triangle.
[math]PBC[/math] is an obtuse triangle.

15. Question

If [math]\cos\theta=k[/math] where [math]\theta[/math] is acute, which of the following expressions is equivalent to [math]\sin\theta[/math]?

[math]k[/math]
[math]1-k[/math]
[math]1-k^2[/math]
[math]\sqrt{1-k^2}[/math]

16. Question

Let [math]ABC[/math] be a right triangle ([math]\angle C[/math] is a right angle). If [math]BC=8[/math] and [math]\cos B=0.4[/math], what is [math]AB[/math]?

17. Question

Which of the following is equal to [math]AD[/math]?

[math]\tan(\angle ABC)-\tan(\angle DBC)[/math]
[math]\tan(\angle ABC)+\tan(\angle DBC)[/math]
[math]\tan(\angle ABC)-\tan(\angle ABD)[/math]
[math]\tan(\angle ABC)+\tan(\angle ABD)[/math]

18. Question

Let [math]\theta[/math] be an acute angle and [math]\theta\neq45^\circ[/math]. If [math]\sin\theta=m[/math], which of the following values is equal to [math]m[/math]?

[math]\sin(90^\circ-\theta)[/math]
[math]\cos(90^\circ-\theta)[/math]
[math]\cos(\theta)[/math]
[math]\tan(90^\circ-\theta)[/math]

19. Question

What is the summation of exterior angles, in radians, of a triangle?

[math]\dfrac{1}{2}\pi[/math]
[math]\pi[/math]
[math]\dfrac{3}{2}\pi[/math]
[math]2\pi[/math]

20. Question

Let [math]ABC[/math] be a right triangle ([math]C[/math] is a right angle). If [math]BC=2[/math] and [math]\angle B=1.4[/math] radians, what is the length of [math]\overline{AC}[/math]?

[math]11.596[/math]
[math]1.971[/math]
[math]2.340[/math]
[math]4.197[/math]

21. Question

Consider a sector [math]OAB[/math] with radius 3. If the length of [math]\overset{\frown}{AB}[/math] is [math]2\pi[/math], what is the distance between [math]A[/math] and [math]B[/math]?

22. Question

Consider a sector [math]OAB[/math] with radius 3. If the length of [math]\overset{\frown}{AB}[/math] is also [math]3[/math], what is the measure,in degrees, of [math]\angle AOB[/math]?

[math]60^\circ[/math]
[math]57^\circ[/math]
[math]53^\circ[/math]
[math]50^\circ[/math]

23. Question

Two sectors have the same area. If the radius of the first sector is twice the radius of the second sector, then what is the ratio of the central angle of the first sector to the central angle of the second sector?

[math]\dfrac{1}{4}[/math]
[math]\dfrac{1}{2}[/math]
[math]2[/math]
[math]4[/math]

24. Question

$$x^2+y^2=2x+2y$$The equation above shows a circle, what is its radius?

[math]1[/math]
[math]\sqrt{2}[/math]
[math]2[/math]
[math]4[/math]

25. Question

If circle [math]C[/math] is always in the second quadrant, which of the following equations could be [math]C[/math]?

[math](x-2)^2+(y+2)^2=2[/math]
[math](x-2)^2+(y+2)^2=5[/math]
[math](x+2)^2+(y-2)^2=2[/math]
[math](x+2)^2+(y-2)^2=5[/math]

26. Question

Let [math]a[/math] be a positive real number. Which of the following circles touches the [math]x[/math]-axis?

[math](x-a)^2+y^2=a[/math]
[math](x-a)^2+y^2=a^2[/math]
[math]x^2+(y-a)^2=a[/math]
[math]x^2+(y-a)^2=a^2[/math]

27. Question

Which of the following points is outside the circle [math]C: (x+3)^2+(y-4)^2=25[/math]?

[math](-3,5)[/math]
[math](6,4)[/math]
[math](0,0)[/math]
[math](-4,3)[/math]

28. Question

In the figure, [math]O[/math] is the center of the circle. If [math]OP=6[/math], what is the radius of the circle?

[math]6\sin70^\circ[/math]
[math]6\cos70^\circ[/math]
[math]6\sin35^\circ[/math]
[math]6\cos35^\circ[/math]

29. Question

Let [math]ABC[/math] be an isosceles triangle. If [math]AB=AC=25[/math] and [math]BC=30[/math], what is the area of triangle [math]ABC[/math]?

[math]600[/math]
[math]375[/math]
[math]300[/math]
[math]250[/math]

30. Question

In the figure, [math]A, B, C, D, E[/math], and [math]F[/math] can form a regular hexagon. If [math]AB=1[/math], what is the length of [math]\overline{DF}[/math]?

31. Question

Let [math]A(1,5), B(1,10)[/math], and [math]C(6,4)[/math] be three points on the [math]xy[/math]-plane. What is the area of triangle [math]ABC[/math]?

32. Question

In the figure, [math]ABC[/math] is a right triangle and [math]ODE[/math] is a sector. If [math]OA=8[/math] and [math]OB=5[/math], what is [math]OD[/math]?

33. Question

What is the volume of a square pyramid whose lateral faces are equilateral triangle with side length [math]2[/math]?

[math]6.928[/math]
[math]3.464[/math]
[math]1.886[/math]
[math]1.155[/math]