DSAT extra practice Ch5 Lv1

What is the area of a piece of pizza with diameter 12 inches?

If the area of a square is 36, what is its perimeter?

Emily has a cylindrical glass and a concical glass. These two glasses have the same radius and height. If the volume of the cylindrical glass is 900 ml, what is the volume, in ml, of the conical glass?

Jonathan has a rectangular box (no top). The base of the box is a square with side [math]x[/math] inches. If the height of the box is 4 inches, what is the volume, in cubic inches, of the box in terms of [math]x[/math]?

Kyle bought a rectangular 27-in screen. The number “27-in” means that the lengths of the diagonal of the screen is 27 inches. If the screen’s base is 23 inches, what is the length, in inches, of its height? Round to the nearest integer.

In the figure, [math]ABED, BCGF[/math], and [math]ACHI[/math] are squares. If the areas of [math]ABED[/math] and [math]BCGF[/math] are 36 and 25 respectively, what is the area of [math]ACHI[/math]?

The figure show a trapezoid [math]ABCD[/math]. [math]E[/math] is the intersection of two diagonals [math]\overline{AC}[/math] and [math]\overline{BD}[/math]. If [math]ED=EA=1[/math] and [math]EB=EC=3[/math], what is the perimeter of [math]ABCD[/math]?

The figure shows a right triangle [math]ABC[/math]. Points [math]D[/math] and [math]E[/math] are on [math]\overline{BC}[/math] that satisfies, [math]BD=DE=EC[/math]. If [math]AB=3[/math] and [math]BC=6[/math], which of the following values is an integer?

Consider a triangle [math]ABC[/math]. If [math]m\angle A=m\angle B=42^\circ[/math], what is the measure of the exterior angle [math]C[/math]?

There are three lines [math]\ell_1, \ell_2[/math], and [math]\ell_3[/math] on a plane. If [math]\ell_1[/math] and [math]\ell_2[/math] is not parallel, which of the following values could not be [math]x[/math]?

In the given figure, [math]\ell_1[/math] is parallel to [math]\ell_2[/math]. What is the value of [math]x[/math]?

The figure shows three lines [math]\ell_1, \ell_2[/math] and [math]\ell_3[/math]. These lines form 8 angles labeled [math]a[/math] to [math]h[/math]. How many angles must be equal to [math]a[/math]?

If quadrilateral [math]ABCD[/math] and quadrilateral [math]SPRQ[/math] are congruent, which of the following values is equal to [math]AB[/math]?

If [math]BC=BP[/math], which of the following conditions added \textbf{cannot} make sure that the two triangles [math]ABC[/math] and [math]RPB[/math] are congruent?

In the figure, triangle [math]ABC[/math] is similar to triangle [math]AQP[/math]. If [math]m\angle C=70^\circ[/math] and [math]m\angle A=60^\circ[/math], what is the measure of [math]\angle AQP[/math] in degrees?

In the figure, [math]P, Q[/math], and [math]R[/math] are the midpoints of [math]\overline{AB}, \overline{AC}[/math] and [math]\overline{BC}[/math] respectively. If the area of triangle [math]PQR[/math] is 20, what is the area of triangle [math]BPR[/math]?

In the figure, [math]\overline{PQ}[/math] is parallel to [math]\overline{BC}[/math]. If [math]CQ=2AQ[/math], which of the following is true?

Which of the following statements must be true?

Which of the following values is equal to zero?

In the figure, triangles [math]ABC[/math] and [math]DEF[/math] are similar. If [math]\sin\theta=0.6[/math], what is the length of [math]\overline{BC}[/math]?

Let [math]a, b,[/math] and [math]c[/math] be three angles satisfying [math]a=1[/math] radian, [math]b=1.5[/math] radians, and [math]c=2[/math] radians. How many angles are obtuse?

Which of the following values is closest to [math]80^\circ[/math]?

Which triangles in the figure has the bigger area?

If [math]108^\circ[/math] is equal to [math]a\pi[/math] radians where [math]a[/math] is a constant, what is the value of [math]a[/math]?

If [math]\cos(20^\circ)=\cos\theta[/math], which of the following values could be [math]\theta[/math]?

If [math]\sin\theta=\dfrac{1}{3}[/math] where [math]\theta[/math] is an acute angle measured in radians, which of the following values is also [math]\dfrac{1}{3}[/math]?

Let [math]ABC[/math] be a triangle. If [math]m\angle A=2[/math] and [math]m\angle B=3[/math], which of the following is true?

If the perimeter of a sector with radius [math]5[/math] and central angle [math]72^\circ[/math] can be written as [math]a+b\pi[/math] where [math]a[/math] and [math]b[/math] are constants, which of the following values is [math]a+b[/math]?

What is the area of a sector whose radius is 6 and the central angle is [math]40^\circ[/math]?

Consider a sector [math]OAB[/math] with radius 10. If the area of [math]OAB[/math] is [math]10\pi[/math], what is its central angle?

In the figure, [math]OAB[/math] is a sector. What is the area of the shade region?

Let [math]A(1,3)[/math] be a point on the [math]xy[/math]-plane. If [math]P(x,y)[/math] is a point that satisfies [math]PA=7[/math], where is [math]P[/math] located on the following equation?

Which of the following equations is a circle?

$$x^2+y^2-4x+9y=0$$The equation above shows a circle, what is the center of the circle?

Let [math]C[/math] be a circle with center [math](1,-3)[/math]. If [math]P(1,3)[/math] is on [math]C[/math], what is the equation of [math]C[/math]?