Curved surface area of a right circular cylindrical log of wood of uniform density is 440 sq`*`dcm. If 1 cubic dcm of wood weight `1*5` kg and weight of the log is `9*24` quintals, then calculate the length of diameter of log and its height.

Explanation

1 quintal `= 100 ` kg
`:.9.24 ` quintal `= 100 xx 9.24 kg = 924 kg`
Also 1.5 kg is the weight of 2 cu.dcm wood
`:.` 1 kg is the weight of `(1)/(1.5)` cu.dcm wood
`:.` 924 kg is the weight of `(1xx924)/(1.5)` cu.dcm wood
`= 616 ` cubic.dcm
Let the radius of the log of wood be r dcm and its height be h dcm.
`:.` curved surface area `= 2 xx (22)/(7) xx r xx h ` sq. dcm As per question, `2xx(22)/(7) xx rh = 440`
`rArr rh = (440xx7)/(2xx 22) rArr rh = 70 ` .......(1)
Also, volume of the log `= (22)/(7) xx r^(2) xx h ` cu-dcm
As per question, `(22)/(7) xx r^(2) xx h = 616 rArr r xx rh = (616xx7)/(22) rArr r xx 70 = 196 [ :' rh = 70 ] rArr r = (196)/(70) = 2.8`
`:. 2 r = 2 xx 2.8 = 5.6` From (1) we get, `h=(70)/(2.8)=25`
Hence the required diameter `= 5.6` dcm and height `= 25` dcm.