A regular right pyramid has a square base with a side length of 12 cm. Its slant height is 8 cm. What is its volume?
254 cm3
The slant height runs from the apex to the midpoint of a base edge, so with the vertical height h and half the base side (6 cm) it forms a right triangle.
\(h = \sqrt{8^2 - 6^2} = \sqrt{64 - 36} = \sqrt{28} = 2\sqrt{7}\) cm.
Base area = 122 = 144 cm2.
Volume = \(\frac{1}{3} \times 144 \times 2\sqrt{7} = 96\sqrt{7} \approx 96 \times 2.6458 \approx 254\) cm3.
Hence, the volume of the pyramid is about 254 cm3.
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Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
