Question

the length of a rectangular carton is twice the breadth and thrice the height .if the volume of the carton is 4500cm cube ,find its length ,breadth ,and height .






Drop thnx plz, will return for sure:-D​

Answer 1

Answer:

According to question, length = 2b = 3h

2b = 3h b = 3h 2 2

Volume= 288 cm3 (3h) / 3h) (h) = 288 3^)(n)=

h3 = 64

h = 4 cm

:: Length: = 3x 4 = 12 cm Breadth = 3/₂ x 4 = 6 cm

Answer 2

Given :

• Length of the rectangular carton is twice the breadth and thrice the height .
• Its Volume is 4500 cm³ .

To Find :

• Find the Dimensions

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Volume{\small_{(Cuboid)}} = Length \times Width \times Height }}}}}$

$\dag$ According to the Question :

$\longmapsto$ Let the Length be y cm .So :

$\qquad \; {\pmb{\sf{ Length = y \; cm }}}$

$\longmapsto$ Length is twice the Width .So :

$\qquad \; {\pmb{\sf{ Breadth = \dfrac{y}{2} \; cm }}}$

$\longmapsto$ Length is thrice the Height .So :

$\qquad \; {\pmb{\sf{ Length = \dfrac{y}{3} \; cm }}}$

$\dag$ Calculating the Value of y :

${\longmapsto{\qquad{\sf{ Volume = Length \times Width \times Height }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 4500 = \dfrac{y}{1} \times \dfrac{y}{2} \times \dfrac{y}{3} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 4500 = \dfrac{y}{1} \times \dfrac{ {y}^{2} }{6} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 4500 = \dfrac{ {y}^{3} }{6} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 4500 \times 6 = {y}^{3} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 27000 = {y}^{3} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \sqrt{27000} = y }}}} \\ \\ \\ \\ \ {\longmapsto \; {\pmb{\underline{\boxed{\pink{\frak{ y = 30 }}}}}}}$

$\dag$ Calculating the Dimensions :

• Length = y = 30 cm
• Breadth = 30/2 = 15 cm
• Height = 30/3 = 10 cm

$\therefore \;$ Length of the Carton is 30 cm ,Breadth is 15 cm and the Height is 10 cm .

$\\ \qquad{\rule{200pt}{2pt}}$