(a) 
The diagram shows a pyramid standing on a cuboid. The dimensions of the cuboid are 4m by 3m by 2m and the slant edge of the pyramid is 5m. Calculet the volume of the shape.
(b) The 2nd, 3rd and 4th terms of an A.P are x – 2, 5 and x + 2 respectively. Calculate the value of x.
Explanation
(a) From the pyramid, construct \(\Delta BFG\) by drawing a line from B to F.
\(|BF|^{2} = 4^{2} + 3^{2}\)
\(|BF| = 25 \implies |BF| = 5m\)
In calculating the height,
\(h^{2} = 5^{2} - (\frac{5}{2})^{2}\)
\(h^{2} = \frac{75}{4}\)
\(h = \sqrt{75}{4}\)
= \(4.33 m\)
Volume of a pyramid = \(\frac{1}{3} \times 4 \times 3 \times 4.33\)
= \(17.32 m^{3}\)
Volume of a cuboid = \(l \times b \times h\)
= \(3 \times 4 \times 2\)
= \(24 m^{3}\)
Total volume of the shape = \(17.32 + 24\)
= \(41.32 m^{3}\)
(b) \(5 - (x - 2) = d\)
\((x + 2) - 5 = d\)
\(\therefore (x + 2) - 5 = 5 - (x - 2)\)
\(x - 3 = 7 - x\)
\(2x = 10\)
\(x = 5\)