Question

Find the volume, the lateral surface are and the total surface area of the cuboid whose dimensions are:
(i) length = 12 cm, breadth = 8 cm and height = 4.5 cm
(ii) length = 26 m, breadth = 14 m and height = 6.5 m
(iii) length = 15 m, breadth = 6 m and height = 5 dm
(iv) length = 24 m, breadth = 25 cm and height = 6 m

Answer 1

(i)
Here, l = 12 cm, b = 8 cm, h = 4.5 cm
Volume of the cuboid = $l\times b\times h$
$$\begin{gathered} =(12\times 8\times 4.5){\mathrm{cm}}^3 \\ =432{\mathrm{cm}}^3 \end{gathered}$$

Total Surface area = 2(lb + lh+ bh)
$$\begin{gathered} =2(12\times 8+12\times 4.5+8\times 4.5){\mathrm{cm}}^2 \\ =2(96+54+36){\mathrm{cm}}^2 \\ =2\times 186{\mathrm{cm}}^2 \\ =372\mathrm{cm}{}^2 \end{gathered}$$

Lateral surface area = $2\left(l+b\right)\times h$
$$\begin{gathered} =\left[2\left(12+8\right)\times 4.5\right]{\mathrm{cm}}^2 \\ =\left[2\left(20\right)\times 4.5\right]{\mathrm{cm}}^2 \\ =40\times 4.5{\mathrm{cm}}^2 \\ =180{\mathrm{cm}}^2 \end{gathered}$$

(ii)
Here, l = 26 m; b = 14 m; h =6.5 m
Volume of the cuboid = $l\times b\times h$
$$\begin{gathered} =\left(26\times 14\times 6.5\right){\mathrm{m}}^3 \\ =2366{\mathrm{m}}^3 \end{gathered}$$

Total surface area = 2(lb + lh+ bh)
$$\begin{gathered} =2(26\times 14+26\times 6.5+6.5\times 14){\mathrm{m}}^2 \\ =2(364+169+91){\mathrm{m}}^2 \\ =2\times 624{\mathrm{m}}^2 \\ =1248{\mathrm{m}}^2 \end{gathered}$$

Lateral surface area = $2\left(l+b\right)\times h$
$$\begin{gathered} =\left[2\left(26+14\right)\times 6.5\right]{\mathrm{m}}^2 \\ =\left[2\times 40\times 6.5\right]{\mathrm{m}}^2 \\ =520{\mathrm{m}}^2 \end{gathered}$$

(iii)
Here, l = 15 m; b = 6 m; h = 5 dm = 0.5 m
Volume of the cuboid = $l\times b\times h$
$$\begin{gathered} =(15\times 6\times 0.5){\mathrm{m}}^3 \\ =45{\mathrm{m}}^3 \end{gathered}$$


Total surface area = 2(lb + lh+ bh)
$$\begin{gathered} =2(15\times 6+15\times 0.5+6\times 0.5){\mathrm{m}}^2 \\ =2(90+7.5+3){\mathrm{m}}^2 \\ =2\times 100.5{\mathrm{m}}^2 \\ =201{\mathrm{m}}^2 \end{gathered}$$

Lateral surface area = $2\left(l+b\right)\times h$
$$\begin{gathered} =\left[2\left(15+6\right)\times 0.5\right]{\mathrm{m}}^2 \\ =\left[2\times 21\times 0.5\right]{\mathrm{m}}^2 \\ =21{\mathrm{m}}^2 \end{gathered}$$

(iv)
Here, l = 24 m; b = 25 cm = 0.25 m; h =6 m
Volume of the cuboid = $l\times b\times h$
$$\begin{gathered} =\left(24\times 0.25\times 6\right){\mathrm{m}}^3 \\ =36{\mathrm{m}}^3 \end{gathered}$$

Total Surface area = 2(lb + lh+ bh)
$$\begin{gathered} =2(24\times 0.25+24\times 6+0.25\times 6){\mathrm{m}}^2 \\ =2(6+144+1.5){\mathrm{m}}^2 \\ =2\times 151.5{\mathrm{m}}^2 \\ =303{\mathrm{m}}^2 \end{gathered}$$

Lateral surface area = $2\left(l+b\right)\times h$
$$\begin{gathered} =\left[2\left(24+0.25\right)\times 6\right]{\mathrm{m}}^2 \\ =\left[2\times 24.25\times 6\right]{\mathrm{m}}^2 \\ =291{\mathrm{m}}^2 \end{gathered}$$