Question

Find the volume, the lateral surface area and the total surface area of the cuboid whose dimensions are:

(i) Length $=12cm$ ,breadth $=8cm$ and height $=4.5cm$

(ii) Length $=26m$, breadth $=14m$ and height $=6.5m$

(iii) Length $=15m$, breadth $=6m$ and height $=5dm$

(iv) Length $=24m$, breadth $=24cm$ and height $=6cm$

Answer 1

(i) Length $=12cm$, breadth $=8cm$ and height $=4.5cm$.

$\therefore$ Volume of cuboid $=l\times b\times h$

$=12\times 8\times 4.5$

$=432c{m}^3$

$\therefore$ Lateral surface area of a cuboid $=2(l+b)\times h$

$=\left[2\right(12+8)\times 4.5]c{m}^2$

$=(2\times 20\times 4.5)c{m}^2$

$=180c{m}^2$

$\therefore$ Total surface area of cuboid $=2(lb+bh+lh)$

$=2(12\times 8)=(8\times 4.5)+(4.5\times 12)c{m}^2$

$=2(96+36+54)c{m}^2$

$=2\left(186\right)c{m}^2=372c{m}^2$

(ii) Length $=26m$, breadth $=14m$ and height $=6.5m$

$\therefore$ Volume of cuboid $=l\times b\times h$

$=(26\times 14\times 6.5)$

$=2366m^3$

$\therefore$ Lateral surface area of a cuboid $=2(l+b)\times h$

$=\left[2\right(26+14)\times 6.5]$

$=(2\times 40\times \times 6.5)=520m^2$

$\therefore$ Total surface area $=2(lb+bh+hl)$

$=2\left(\right(26\times 14)+(14\times 6.5)+(6.5\times 26\left)\right)$

$=2(364+91+169)=(2\times 624)m^2=1248m^2$

(iii) Length $=15m$, breadth $=6m$ and height $=5dm=0.5m$.

$\therefore$ Volume of the cuboid $=l\times b\times h$

$=(15\times 6\times 0.5)m^3$

$=45m^3$

$\therefore$ Lateral surface area of a cuboid $=2(l+b)\times h$

$=\left[2\right(15+6)\times 0.5]$

$=(2\times 21\times 0.5)=21m^2$

$\therefore$ Total surface area $=2(lb+bh+hl)$

$=2\left(\right(15\times 6)+(6\times 0.5)+(0.5\times 15\left)\right)$

$=2(90+3+7.5)=(2\times 100.5)m^2=201m^2$

(iv) Length $=24m$, breadth $=0.25m$ and height $=6m$.

$\therefore$ Volume of the cuboid $=l\times b\times h$

$=(24\times 0.25\times 6)m^3$

$=36m^3$

$\therefore$ Lateral surface area of a cuboid $=2(l+b)\times h$

$=\left[2\right(24+0.25)\times 6]$

$=(2\times 24.25\times 6)m^2=291m^2$

$\therefore$ Total surface area $=2(lb+bh+hl)$

$=2\left(\right(24\times 0.25)+(0.25\times 6)+(24\times 6\left)\right)$

$=2(6+1.5+144)=(2\times 151.5)=303m^2$