Question

If the length of a cuboid is 60cm and width 40cm and its surface area is 14800cm² find its height

Answer 1

Answer:

The height of cuboid is 50 cm.

Step-by-step explanation:

Given :

• ➺ Length of cuboid = 60cm
• ➺ Width of cuboid = 40cm.
• ➺ Surface area of cuboid = 14800cm²

To Find :

• ➺ Height of cuboid

Using Formulas :

$\star\small{\underline{\boxed{\sf \pink{SA_{(Cuboid)} = 2(lb + bh + lh)}}}}$

• »» SA = surface area
• »» l = length
• »» b = breadth
• »» h = height

Solution :

Substituting all the given values in the formula to find height of cuboid :

${\longrightarrow{\sf{SA_{(Cuboid)} = 2(lb + bh + lh)}}}$

${\longrightarrow{\sf{14800= 2(60 \times 40 + 40 \times h + 60 \times h)}}}$

${\longrightarrow{\sf{14800= 2(2400 + 40h + 60h)}}}$

${\longrightarrow{\sf{14800= 2(2400 + 100h)}}}$

${\longrightarrow{\sf{14800= 4800 + 200h}}}$

${\longrightarrow{\sf{200h = 14800 - 4800}}}$

${\longrightarrow{\sf{200h = 10000}}}$

${\longrightarrow{\sf{h = \dfrac{10000}{200}}}}$

${\longrightarrow{\sf{h = \cancel{\dfrac{10000}{200}}}}}$

${\longrightarrow{\sf{\underline{\underline{\red{h = 50 \: cm}}}}}}$

Hence, the height of cuboid is 50 cm.

$\underline{\rule{220pt}{3.5pt}}$

Answer 2

Formula of surface area of cuboid = 2(lb+bh+lh) . Surface area of cuboid is 14800cm^2 (Given) then 14800 = 2(60*40+40*Height+Height*60) 14800= 2(2400+40*H+H*60) 14800= 4800+80*2H+2H*60 14800= 4880*4H*60 14800/4880*60= 4H
14800/292800=4H
7400/146400=4H
3700/73200=4H
1850/36600=4H
925/18300=4H
185/3660=4H
37/732=4H
37/732*4=H
37/2928=H
H= 79.1351351