GED Math - How to Get the Right Answers on the 2024 Test (1) - Free Printable

We are given a cone-shaped drinking cup with:

- Diameter = $ 2\frac{3}{4} $ inches
- Height = 4 inches

We are to find the volume of the cone, rounded to the nearest tenth of a cubic inch.

---

🔷 Step 1: Recall the formula for the volume of a cone

$$
V = \frac{1}{3} \pi r^2 h
$$

Where:
- $ r $ is the radius of the base
- $ h $ is the height
- $ \pi \approx 3.1416 $

---

🔷 Step 2: Find the radius

The diameter is $ 2\frac{3}{4} $ inches.

Convert to an improper fraction:

$$
2\frac{3}{4} = \frac{11}{4} \text{ inches}
$$

So the radius is half of that:

$$
r = \frac{11}{4} \div 2 = \frac{11}{8} \text{ inches}
$$

---

🔷 Step 3: Plug into the volume formula

$$
V = \frac{1}{3} \pi \left(\frac{11}{8}\right)^2 (4)
$$

First, square the radius:

$$
\left(\frac{11}{8}\right)^2 = \frac{121}{64}
$$

Now plug in:

$$
V = \frac{1}{3} \pi \cdot \frac{121}{64} \cdot 4
$$

Simplify:

$$
= \frac{1}{3} \cdot \frac{121}{64} \cdot 4 \cdot \pi
= \frac{121}{64} \cdot \frac{4}{3} \cdot \pi
= \frac{121 \cdot 4}{64 \cdot 3} \cdot \pi
= \frac{484}{192} \cdot \pi
$$

Simplify $ \frac{484}{192} $:

Divide numerator and denominator by 4:

$$
\frac{121}{48} \cdot \pi
$$

Now calculate:

$$
\frac{121}{48} \approx 2.5208
$$

Multiply by $ \pi $:

$$
V \approx 2.5208 \cdot 3.1416 \approx 7.914
$$

Round to the nearest tenth:

$$
V \approx 7.9 \text{ cubic inches}
$$

---

✔ Final Answer:

B. 7.9

---

✔ Answer: B. 7.9