📌 Step 1: Recall the volume formula for a cylinder
V = πr²h

📌 Step 2: Plug in the values
r = 3 ft, h = 8 ft, π ≈ 3.14
V = 3.14 × 3² × 8 = 3.14 × 9 × 8

📌 Step 3: Calculate
3.14 × 9 = 28.26
28.26 × 8 = 226.08 ft³

💡 Tip: Always check your units — volume is measured in cubic units (ft³, cm³, m³).

📌 Step 1: Identify the shape
A pizza box is a rectangular prism (cuboid).

📌 Step 2: Apply the volume formula
V = length × width × height
V = 14 × 14 × 2

📌 Step 3: Calculate
= 392 in³

💡 Quick check: Volume is always in cubic units. If your answer is in square units, something went wrong!

📌 Step 1: Recall the area formula for a regular polygon
A = ½ × perimeter × apothem

📌 Step 2: Find the perimeter
Perimeter = 6 sides × 6 cm = 36 cm

📌 Step 3: Calculate the area
A = ½ × 36 × 5.2 = 18 × 5.2 = 93.6 cm²

💡 What's an apothem? The distance from the center to the midpoint of a side. It's always perpendicular to the side.

📌 Step 1: Understand permutations
Arranging n objects in a line uses n! (n factorial).

📌 Step 2: Calculate 5!
5! = 5 × 4 × 3 × 2 × 1

📌 Step 3: Solve step by step
5 × 4 = 20
20 × 3 = 60
60 × 2 = 120
120 × 1 = 120

💡 Key difference:
• Permutation = order matters (arranging in a line)
• Combination = order doesn't matter (choosing a team)
• Formula: P(n,r) = n!/(n-r)! and C(n,r) = n!/(r!(n-r)!)

📌 Step 1: Understand cross sections
A cross section is the shape you get when you "slice" a 3D object with a flat plane.

📌 Step 2: Visualize the cut
Slicing a cylinder parallel to its base is like cutting a log straight across.

📌 Step 3: Determine the shape
The base of a cylinder is a circle. A parallel cut produces the exact same shape → Circle

💡 Cross section rules:
• Cut parallel to base → same shape as base
• Cut perpendicular to base of cylinder → rectangle
• Cut at an angle through cylinder → ellipse

Step 1: Translate 6 right → add 6 to x: W(−4,2) → (−4+6, 2) = (2, 2).
Step 2: Reflect over x-axis → negate y: (2, 2) → (2, −2).
So W′ = (2, −2).

📌 Step 1: Recall the central angle-arc relationship
A central angle equals its intercepted arc.

📌 Step 2: Apply
Central angle = 90° → Arc = 90°

💡 Key relationships in circles:
• Central angle = intercepted arc
• Inscribed angle = ½ × intercepted arc
• Two inscribed angles intercepting the same arc are equal

📌 Step 1: Find the rotational symmetry angle
For a regular n-sided polygon:
Smallest rotation = 360° / n

📌 Step 2: Apply to a pentagon (n = 5)
360° / 5 = 72°

📌 Answer: 72°

💡 Tip: A figure has rotational symmetry if it maps onto itself after a rotation less than 360°. A regular pentagon maps to itself at 72°, 144°, 216°, and 288°.