Geometry Test Questions on Volume of Pyramids (Formula Application)

📚 Quick Study Guide

📐 The volume of a pyramid is the amount of space it occupies. 📏 To calculate volume, you'll need the area of the base (B) and the height (h) of the pyramid. ➗ The formula for the volume (V) of a pyramid is: $V = \frac{1}{3}Bh$. ✏️ For a square pyramid, the base area $B = s^2$ where $s$ is the side length of the square base. So, $V = \frac{1}{3}s^2h$. 🔺 For a triangular pyramid, the base area depends on the type of triangle. If it's an equilateral triangle, $B = \frac{\sqrt{3}}{4}a^2$ where $a$ is the side length, so $V = \frac{1}{3}(\frac{\sqrt{3}}{4}a^2)h$. 💡 Always ensure your units are consistent (e.g., all in cm, m, or inches) before calculating the volume. Volume is expressed in cubic units (e.g., cm³, m³, in³).

Practice Quiz

1. A square pyramid has a base side length of 6 cm and a height of 8 cm. What is its volume?
   1. 144 cm³
   2. 96 cm³
   3. 288 cm³
   4. 48 cm³
2. A pyramid has a rectangular base with sides 4 m and 5 m, and a height of 9 m. What is its volume?
   1. 60 m³
   2. 180 m³
   3. 120 m³
   4. 90 m³
3. The volume of a pyramid is 100 cm³ and its base area is 25 cm². What is its height?
   1. 12 cm
   2. 4 cm
   3. 8 cm
   4. 3 cm
4. A triangular pyramid has a base area of 15 in² and a height of 7 in. What is its volume?
   1. 35 in³
   2. 105 in³
   3. 52.5 in³
   4. 70 in³
5. A square pyramid has a volume of 48 m³ and a height of 9 m. What is the side length of its square base?
   1. 4 m
   2. 16 m
   3. 2 m
   4. 8 m
6. A pyramid has a base area of 36 ft² and a height equal to one-third of the side of the base. What is the volume if the base is a square?
   1. 36 ft³
   2. 72 ft³
   3. 108 ft³
   4. 12 ft³
7. If the height of a pyramid is doubled, what happens to its volume, assuming the base stays the same?
   1. The volume stays the same
   2. The volume is halved
   3. The volume is doubled
   4. The volume is quadrupled