📐 Geometry Circles And Pop (12 Focused Problems)
Recommended: 30–40 minutes. No calculator.
Problems
1.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #1
What is the area of a triangle with base 6 and height 8?
A) $12$ B) $24$ C) $36$ D) $48$ E) $64$
Answer & Solution
Answer: B
The area is $\frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 6 \cdot 8 = 24$.
2.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #2
What is the circumference of a circle with radius 5?
A) $5\pi$ B) $10\pi$ C) $25\pi$ D) $50\pi$ E) $100\pi$
Answer & Solution
Answer: B
The circumference is $2\pi r = 2\pi \cdot 5 = 10\pi$.
3.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #3
What is the area of a circle with diameter 8?
A) $8\pi$ B) $16\pi$ C) $32\pi$ D) $64\pi$ E) $128\pi$
Answer & Solution
Answer: B
The radius is $\frac{8}{2} = 4$, so the area is $\pi r^2 = \pi \cdot 4^2 = 16\pi$.
4.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #4
What is the volume of a cube with side length 3?
A) $9$ B) $18$ C) $27$ D) $36$ E) $54$
Answer & Solution
Answer: C
The volume is $s^3 = 3^3 = 27$.
5.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #5
What is the surface area of a cube with side length 4?
A) $48$ B) $64$ C) $96$ D) $128$ E) $192$
Answer & Solution
Answer: C
The surface area is $6s^2 = 6 \cdot 4^2 = 6 \cdot 16 = 96$.
6.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #6
What is the area of a triangle with base 6 and height 8?
A) $12$ B) $24$ C) $36$ D) $48$ E) $64$
Answer & Solution
Answer: B
The area is $\frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 6 \cdot 8 = 24$.
7.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #7
What is the circumference of a circle with radius 5?
A) $5\pi$ B) $10\pi$ C) $25\pi$ D) $50\pi$ E) $100\pi$
Answer & Solution
Answer: B
The circumference is $2\pi r = 2\pi \cdot 5 = 10\pi$.
8.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #8
What is the area of a circle with diameter 8?
A) $8\pi$ B) $16\pi$ C) $32\pi$ D) $64\pi$ E) $128\pi$
Answer & Solution
Answer: B
The radius is $\frac{8}{2} = 4$, so the area is $\pi r^2 = \pi \cdot 4^2 = 16\pi$.
9.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #9
What is the volume of a cube with side length 3?
A) $9$ B) $18$ C) $27$ D) $36$ E) $54$
Answer & Solution
Answer: C
The volume is $s^3 = 3^3 = 27$.
10.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #10
What is the surface area of a cube with side length 4?
A) $48$ B) $64$ C) $96$ D) $128$ E) $192$
Answer & Solution
Answer: C
The surface area is $6s^2 = 6 \cdot 4^2 = 6 \cdot 16 = 96$.
11.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #11
What is the area of a triangle with base 6 and height 8?
A) $12$ B) $24$ C) $36$ D) $48$ E) $64$
Answer & Solution
Answer: B
The area is $\frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 6 \cdot 8 = 24$.
12.
Tags: Geometry · Difficulty (E/M/H) · source: AMC10 2020 #12
What is the circumference of a circle with radius 5?
A) $5\pi$ B) $10\pi$ C) $25\pi$ D) $50\pi$ E) $100\pi$
Answer & Solution
Answer: B
The circumference is $2\pi r = 2\pi \cdot 5 = 10\pi$.
Answer Key
| # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ans | A | A | A | A | A | A | A | A | A | A | A | A |