Volume of Pyramid and Cone

In general, Volume = base area × perpendicular height

Square-based Pyramid:

Volume = \( \frac{1}{3} \scriptsize \; \times \; base \; area \; \times \; height \)

Volume = \( \frac{1}{3} \scriptsize \; b^2 h\)

Example 9.7.1:

The height of a pyramid on square base is 15 cm. if the volume is 80 cm³ , find the area of the square base.

Solution

• Volume of pyramid = 80 cm³
• Height of a pyramid , h = 15 cm
• b = ?

Volume of pyramid = \( \frac{1}{3} \scriptsize \; b^2 h\)

⇒ \( \scriptsize 80 = \normalsize \frac{1}{3} \scriptsize \: \times \: b^2 \: \times \: 15\)

⇒ \( \scriptsize b^2 = \normalsize \frac{80 \: \times \: 3}{15} \)

⇒ \( \scriptsize b^2 = 16 \)

⇒ \( \scriptsize b = \sqrt{16} \)

⇒ \( \scriptsize b = 4 \: cm\)

∴ Area of the square base = 4 × 4 = 16 cm²