Geometry — Semester B Practice

Question 1 of 9

TEKS 1A-1G Easy Calc Word

A cylindrical water tank has a radius of 3 feet and a height of 8 feet. What is the volume of the tank? (Use π ≈ 3.14)

A 226.08 ft³

B 75.36 ft³

C 301.44 ft³

D 150.72 ft³

Explanation

📌 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).

Question 2 of 9

TEKS 3A-3D Medium Calc Word Diagram

Trapezoid WXYZ has vertices W(−4, 2), X(−1, 2), Y(0, −1), and Z(−5, −1). It is translated 6 units right, then reflected over the x-axis. What are the coordinates of W′?

A W′(10, −2)

B W′(−4, −2)

C W′(2, −2)

D W′(2, 2)

Explanation

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).

Question 3 of 9

TEKS 1A-1G Easy Calc Word

A pizza box is 14 inches on each side and 2 inches tall. What is the volume of the box?

A 392 in³

B 196 in³

C 448 in³

D 280 in³

Explanation

📌 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!

Question 4 of 9

TEKS 13A-13E Medium Calc Word

A card is drawn from a standard 52-card deck. What is the probability of drawing a heart or a king?

A 17/52

B 16/52

C 13/52

D 4/52

Explanation

📌 Step 1: Use the Addition Rule
P(A or B) = P(A) + P(B) − P(A and B)

📌 Step 2: Count each
• Hearts: 13 cards
• Kings: 4 cards
• King of Hearts (counted in both): 1 card

📌 Step 3: Calculate
P = 13/52 + 4/52 − 1/52 = 16/52 = 4/13

💡 Why subtract? The King of Hearts is both a heart AND a king, so it gets counted twice. We subtract once to avoid double-counting.

Question 5 of 9

TEKS 12A-12E Easy Calc Word

A central angle of a circle is 90°. What is the measure of the intercepted arc?

A 45°

B 270°

C 90°

D 180°

Explanation

📌 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

Question 6 of 9

TEKS 13A-13E Easy Calc Word

In how many ways can 5 students be arranged in a line?

A 120

B 25

C 720

D 60

Explanation

📌 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)!)

Question 7 of 9

TEKS 10A-10B Easy Word

What shape is the cross section when a plane cuts through a cylinder parallel to its base?

A Triangle

B Circle

C Ellipse

D Rectangle

Explanation

📌 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°.

Question 8 of 9

TEKS 11A-11D Easy Calc Word

A regular hexagon has a side length of 6 cm and an apothem of 5.2 cm. What is its area?

A 78.0 cm²

B 108.0 cm²

C 93.6 cm²

D 62.4 cm²

Explanation

📌 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.

Question 9 of 9

TEKS 3A-3D Easy Calc Word

Point A(3, 2) is reflected across the x-axis. What are the coordinates of the image?

A (2, 3)

B (−3, −2)

C (−3, 2)

D (3, −2)

Explanation

📌 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

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