Welcome to your ACT 1 Geo: Understand relationships between

$Q_{1}:$ Let $ABCDEF \sim KLMNOP$. If the perimeter of the first hexagon is $66$ ft and the perimeter of the second is $72$ ft, what is the ratio of their areas?

$Q_{2}:$ The surface areas of two similar right cylinders are $80\pi$ $in^{3}$ and $120\pi $ $in^{3}$, respectively. What is the ratio of their volumes?

$Q_{3}:$ A rectangular prism has a length of $15$cm, a width of $9 $cm, and a height of $6 $cm. If each dimension is divided by $3$, what is the ratio of the volume of the original prism to the second prism?

$Q_{4}:$ If two similar octagons have a scale factor of $3:5$, then the ratio of their areas is

$Q_{5}:$ A special garden design requires that the garden have three distinct square sections whose areas follow the ratio $2:3:5$. If such a garden is designed to have a total area of $1550$ square feet, then what would be the area of the smallest section in square feet?

$Q_{6}:$ Each side of square $A$ has a length of $3$ meters, while each side of square $B$ has a length of $9$ meters. What is the ratio of the area of square $A$ to the area of square $B$?

$Q_{7}:$ A rectangle has sides of length $x$ and $x + 1$, where $x$ is a positive number. If the area of the rectangle is $12$, then which of the following is equivalent to the ratio of $x$ to $x + 1$?

$Q_{8}:$ If the sides of two rectangles are in the ratio $4 : 8$, what is the ratio of their areas?

$Q_{9}:$ In the figure shown below, the four squares have the same center. What is the ratio of the perimeter of the outermost square to the perimeter of the innermost square?

$Q_{10}:$ In the $xy$‑plane below, a point (not shown) with coordinates $(a, b)$ lies on the graph of the linear function $h$. If $a$ and $b$ are positive integers, what is the ratio of $a$ to $b$?

$Q_{11}:$ Isosceles trapezoid $JKLM$ is shown below. If the dimensions of trapezoid $JKLM$ are multiplied by a scale factor of f to create trapezoid $J′K′L′M′$, which statement is true?

$Q_{12}:$ If a sphere and a right circular cone have the same radius and equal volumes, what is the ratio of the height of the cylinder to its radius?

$Q_{13}:$ What is the ratio of the circumference of a circle to its radius?

$Q_{14}:$ In rhombus $PQRS$, the ratio of $m\angle P$ to $m \angle Q$ is $1$ to $5$ and $PQ = 6$. What is the area of the rhombus?

$Q_{15}:$ If the interior angles of a pentagon are in the ratio of $2 : 3 : 3 : 5 : 5$, what is the measure of the smallest angle?

$Q_{16}:$ In the diagram below, the circle is inscribed in square $ABCD$, and square $PQRS$ is inscribed in the circle. What is the ratio of the area of the large square to the area of the small square?

$Q_{17}:$ In the figure below, the ratio of the measure of arc $AB$ to the measure of arc $BC$ to the measure of arc $CA$ is $4$ to $3$ to $5$. What is $m\angle A$?

$Q_{18}:$ In the figure below, circle $O$ is tangent to sides $\overline{AD}$ and $\overline{BC}$ of rectangle $ABCD$. If the area of the shaded region is $3$ times the area of the circle, what is the ratio of the length of side $\overline{AD}$ to the circumference of the circle?

$Q_{19}:$ The base of pyramid $1$ is a $3-4-5$ triangle, and the base of pyramid $2$ is a square whose sides are $3$. If the volumes of the pyramid are equal, what is the ratio of the height of pyramid $1$ to the height of pyramid $2$?

$Q_{20}:$ If the volume of a sphere is equal to the volume of a cube, what is the ratio of the edge of the cube to the radius of the sphere?

$Q_{21}:$ In Figure below shows two right circular cylinders, $C$ and $C′$. If $r = kr′$ and $h = kh′$, then what is the ratio of Volume of $C$ to Volume of $C'$?

$Q_{22}:$ In the circle above, chord $RS$ is parallel to diameter $PQ$. If the length of $RS$ is $\frac{3}{ 4}$ of the length of $PQ$ and the distance between the chord and the diameter is $2 \sqrt{7}$, what is the radius of the circle?

$Q_{23}:$ The length and width of a large picture are respectively $18$ inches and $12$ inches. If each dimension is reduced by $x$ inches to make the ratio of length to width $5$ to $3$, what is the value of $x $?

$Q_{24}:$ If triangle $ABC$ is similar to triangle $DEF$ and the segments are given as marked, then $EH$ is equal to ?