Question

The lateral surface area of a cuboid is 324 cmIts height is 9 cm, breadth is 5 cm. Find the volume of the cuboid. ​

Answer 1

Answer:

Here you go mate

Step-by-step explanation:

Volume :- lbh

9x5x9= 405

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

• Lateral surface area of cuboid = 324 $\rm \:cm^2$

• Height of cuboid, h = 9 cm

• Breadth of cuboid, b = 5 cm

Let assume that

• Length of cuboid = $l$ cm

We know,

Lateral surface area of cuboid of length l, breadth b and height h is given by

$\boxed{ { \:LSA_{(Cuboid)} \: = \: {2 \times (l + b) \times h} \: }}$

So, on substituting the values, we get

$\: 2(l + 5) \times 9 = 324$

$\: 2(l + 5)= 36$

$\: l + 5= 18$

$\implies \:l \: = \: 13 \: cm \:$

We know, Volume of cuboid of length l, breadth b and height h is given by

$\boxed{ { \:Volume_{(Cuboid)} \: = \: l \times b \times h \: }}$

So, on substituting the values, we get

$\: Volume_{(Cuboid)} \: = \: 13 \times 5 \times 9$

$\rm\implies \:\boxed{ \bf{ \:Volume_{(Cuboid)} = 585 \: {cm}^{3} \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$