Find the volume of iron required to construct an open box whose external dimensions are 36cm,25cm,and 16.5cm,provided that the thickness of the metal is 1.5cm.If1cm cube of iron weight 7.5g find the weight of the box.
External volume of box= (36*25*16.5)cm cube
= 14850 cm cube
Again,
Internal volume of box where,
Length= (36 - (1.5*2)) = (36-3) = 33 cm
Breadth= (25-(1.5*2)) = (25 - 3)= 22 cm
Height = (16.5 - (1.5 *2)) =(16.5 - 3) = 13.5 cm
then inner volume = (33*22*13.5) = 9801cm cube
Volume of iron = (14850 - 9801) = 5049cm cube
1cm cube weight 7.5 g ,then weight of 5049cm cube = 37867.5 g.-ANS.
Math but iam a student of class8 in manav bharti national school - Shubham Raj from a, Thursday, January 5, 2017 at 9:56pm
External volume of box= (36*25*16.5)cm cube
= 14850 cm cube
Again,
Internal volume of box where,
Length= (36 - (1.5*2)) = (36-3) = 33 cm
Breadth= (25-(1.5*2)) = (25 - 3)= 22 cm
Height= (16.5 - 1.5) = 15 cm
Inner volume = ( 33*22*15) = 10890cm cube
Volume of iron = (14850 - 10890) = 3960 cm cube.
Weight of box = (3960 * 7.5)g = 29700g or (29700/1000) kg.
To find the volume of iron required to construct the box, we need to calculate the difference in volume between the external dimensions of the box and the internal dimensions.
The external dimensions of the box are given as 36cm, 25cm, and 16.5cm. We need to subtract twice the thickness of the metal from each dimension to find the internal dimensions of the box.
So, the internal dimensions can be calculated as follows:
Internal length = External length - 2 x Thickness
Internal width = External width - 2 x Thickness
Internal height = External height - 2 x Thickness
Plugging in the values, we get:
Internal length = 36cm - 2 x 1.5cm = 33cm
Internal width = 25cm - 2 x 1.5cm = 22cm
Internal height = 16.5cm - 2 x 1.5cm = 13.5cm
Now, we can calculate the volume of the iron required by subtracting the internal volume from the external volume.
External volume = External length x External width x External height
Internal volume = Internal length x Internal width x Internal height
Calculating the volumes, we have:
External volume = 36cm x 25cm x 16.5cm = 14850 cm^3
Internal volume = 33cm x 22cm x 13.5cm = 9909 cm^3
To find the volume of iron required, we take the difference between the external and internal volumes:
Volume of iron = External volume - Internal volume
= 14850 cm^3 - 9909 cm^3
= 4941 cm^3
Since the weight of 1 cm^3 of iron is given as 7.5g, we can calculate the weight of the box using the volume of iron:
Weight of the box = Volume of iron x Weight of 1 cm^3 of iron
= 4941 cm^3 x 7.5g/cm^3
= 37057.5g
= 37.0575 kg
Therefore, the weight of the box is approximately 37.0575 kg.
outside volume
= 36(25)(16.5) cm^3
= 14850 cm^2
volume of inner part (the empty space)
= 33(22)(13.5) cm^2
= 9801 cm^3
volume of iron = 14850 - 9801
= 5049 cm^3
1 cm^3 weighs 7.5 kg
so weight of box = .....