Question

. Curved surface area of a right circular cylindrical log of wood of uniform density is 440 sq
dcm. If 1 cubic dcm of wood weighs 1.5 kg and weight of the log is 9.24 quintals. Let us
write by calculating the length of diameter of log and its height.​

Answer 1

Given,

CSA of the right circular cylindrical log of wood = 440 dcm²

Weight of 1dcm³ of wood = 1.5 kg

Weight of the log = 9.24 quintals = 924 kg

To find,

The length of diameter and height of the wooden log.

Solution,

Let,the length of the height of the wooden log = h dcm

And,the radius of the wooden log = r dcm

[Assume,h and r as variables to do the further mathematical calculations.]

Now,

Volume of 1.5 kg wood = 1 dcm³

Volume of 1 kg wood = 1/1.5 dcm³

Volume of 924 kg wood = 924/1.5 = 616 dcm³

So,the volume of the wooden log is 616 dcm³.

Now, the CSA of the wooden log according to the assumed variables = 2πrh dcm²

Now,the volume of the wooden log according to the assumed variables = πr²h dcm³

So,if we compare the values,

1) 2πrh = 440

h = 440/2πr

2) πr²h = 616

h = 616/πr²

Now,if we compare the two values of "h",we will get the following mathematical equation,

616/πr² = 440/2πr

616/πr² = 220/πr

616πr = 220πr²

616πr/220πr² = 1

616/220r = 1

220r = 616

r = 2.8

Diameter = 2 × 2.8 = 5.6 dcm

Now,

2×22/7×2.8×h = 440

17.6h = 440

h = 25

Hence,the diameter of the wooden log is 5.6 dcm and height of the wooden log is 25 dcm.