💡 Common mistake: Don't forget to divide by 3! A cone is 1/3 the volume of a cylinder with the same base and height.
Question 3 of 10
Florida standards 7A-7BMedium Calc Word Diagram
A tree casts a shadow 18 feet long. At the same time, a 5-foot-tall fence post casts a shadow 3 feet long. How tall is the tree?
A30 feet
B36 feet
C24 feet
D27 feet
Explanation
The tree and fence post form similar triangles with their shadows (same sun angle). tree height / tree shadow = fence height / fence shadow h / 18 = 5 / 3 h = 18 × 5/3 = 30 feet.
Question 4 of 10
Florida standards 1A-1GMedium Calc Word Diagram
A kite is flying at the end of a 200-foot string. The string makes a 55° angle with the ground. How high above the ground is the kite? Round to the nearest foot. (sin 55° ≈ 0.819)
A141 feet
B164 feet
C186 feet
D115 feet
Explanation
📌 Step 1: Identify the trig ratio We know the hypotenuse (200 ft) and want the opposite side (height). Use sine: sin = opposite / hypotenuse
📌 Step 2: Set up and solve sin(55°) = h / 200 0.819 = h / 200 h = 200 × 0.819 = 163.8
📌 Answer: ≈ 164 feet
💡 Tip: Angle of elevation from ground = angle between the string and the horizontal, NOT the vertical.
Question 5 of 10
Florida standards 1A-1GHard Calc Word
A composite figure is made of a rectangle (10 m × 6 m) with a semicircle attached to one of the shorter sides. What is the total area? (Use π ≈ 3.14)
A74.1 m²
B102.5 m²
C64.7 m²
D88.3 m²
Explanation
📌 Step 1: Break into simple shapes Rectangle: 10 m × 6 m Semicircle: radius = 6/2 = 3 m (attached to the 6 m side)
📌 Step 2: Calculate each area Rectangle = 10 × 6 = 60 m² Semicircle = ½πr² = ½ × 3.14 × 3² = ½ × 28.26 = 14.13 m²
📌 Step 3: Add them Total = 60 + 14.13 = 74.13 ≈ 74.1 m²
💡 Strategy for composite figures: Always break them into shapes you know (rectangles, triangles, circles), calculate each, then add (or subtract for holes).
Question 6 of 10
Florida standards 11A-11DMedium Calc Word Diagram
A swimming pool has the shape shown below — a rectangle with a semicircle on each end. Find the total area of the pool. (Use π ≈ 3.14)
A356.0 m²
B278.5 m²
C200.0 m²
D257.0 m²
Explanation
Rectangle area = 20 × 10 = 200 m². Two semicircles = one full circle with r = 5: π × 5² = 3.14 × 25 = 78.5 m². Total = 200 + 78.5 = 278.5 m².
Question 7 of 10
Florida standards 12A-12EMedium Calc Word Diagram
A tangent line touches circle O at point T. OT = 5 and the external point P is 13 units from the center O. What is the length of tangent segment PT?
A12
B10
C8
D14
Explanation
The tangent is perpendicular to the radius at the point of tangency. Using the Pythagorean theorem: PT = √(OP² − OT²) = √(13² − 5²) = √(169 − 25) = √144 = 12.
Question 8 of 10
Florida standards 7A-7BMedium Calc Word Diagram
In the figure below, DE ∥ BC. If AD = 4, DB = 6, and AE = 5, find EC.
A6.0
B8.0
C7.5
D10.0
Explanation
📌 Step 1: Apply the Triangle Proportionality Theorem Since DE ∥ BC: AD/DB = AE/EC
Jake claims: "If a quadrilateral has four right angles, then it must be a square." Which figure below is a counterexample?
ARectangle
BRhombus
CSquare
DTrapezoid
Explanation
A rectangle has four right angles but is NOT necessarily a square (it can have unequal side lengths). The rectangle with sides 90×60 is a counterexample to Jake's claim.
Question 10 of 10
Florida standards 3A-3DEasy Calc Word Diagram
Which of the following figures has BOTH reflectional and rotational symmetry?
AA (Scalene triangle)
BD (Arrow)
CC (Parallelogram)
DB (Regular hexagon)
Explanation
📌 Step 1: Check each figure
A (Scalene triangle): No lines of symmetry, no rotational symmetry ✗ B (Regular hexagon): 6 lines of symmetry + rotational symmetry at 60° ✓ C (Parallelogram): No lines of symmetry, rotational symmetry at 180° only → partial ✗ D (Arrow): 1 line of symmetry (vertical) but no rotational symmetry ✗
📌 Answer: B (Regular hexagon)
💡 Tip: All regular polygons have BOTH reflectional AND rotational symmetry. The number of symmetry lines = number of sides.