Question

Pls help meh solve this pls SHOW YOUR WORK !! pLS SHOW YOUR WORK !!

Answer 1

QuestioN :

This Rectangle prism has a volume of 192 cm³. What is its height ?

GiveN :

• Length of Rectangular is 8 Cm.
• Breadth of Rectangular is 6 Cm.
• Height of Rectangular is H Cm.

SolutioN :

Let,

• Length of Rectangular is L Cm.
• Breadth of Rectangular is B Cm.
• Height of Rectangular is H Cm.

★ Diagram.

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(5.6,5.6){ A }\put(11.1,5.8){ B }\put(11.08,8.9){ C }\put(5.46,8.7){ D }\put(3.55,10.15){ E }\put(3.55,7.15){ F }\put(9.14,10.235){ H }\put(9.14,7.3){ G }\put(3.3,6.3){ 6\:Cm }\put(7.75,6.2){ 8\:Cm }\put(11.1,7.5){ H\:Cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

We know,

$\tt \dagger \: \: \: \: \: Volume \: Of \: Rectangular \: prism = L\times B \times H$

$\tt : \implies Volume \: Of \: Rectangular\: prism = 192 {cm}^{2}$

$\tt : \implies \: 192 = 8 \times 6 \times H.$

$\tt : \implies 192 = 48H .$

$\tt : \implies H = \dfrac{\cancel{192}}{\cancel{48}}$

$\tt : \implies H = 4 \: cm.$

Therefore, the height of Rectangular prism is 4 Cm.

Some More information :

• TSA of Cuboid → 2( LB + BH + HL )
• CSA of Cuboid → 2( L + B )H
• Volume of Cuboid → L * B * H.