Find the surface area and the volume of a rectangular solid measuring 5 m by 4 m by 3 m. Also find the length of a diagonal.

In a rectangular solid,

Let l = 5 m, b = 4 m and h = 3 m

By formula,

Surface area of rectangular solid = 2(lb + bh + lh)

= 2(5 × 4 + 4 × 3 + 5 × 3)

= 2(20 + 12 + 15)

= 2 × 47

= 94 m²

Volume of rectangular solid = l × b × h

= 5 × 4 × 3

= 60 m³.

Diagonal of cuboid = $\sqrt{l^2 + b^2 + h^2}$

$= \sqrt{5^2 + 4^2 + 3^2} \\[1em] = \sqrt{25 + 16 + 9} \\[1em] = \sqrt{50} \\[1em] = 5\sqrt{2} \\[1em] = 5 \times 1.414 \\[1em] = 7.07 \text{ m}.$

Hence, surface area = 94 m², volume = 60 m³ and the length of diagonal is 7.07 m.