There are two cylindrical wooden logs as shown in pic. (i) and pic. (ii), the length and diameter of each being 21m. and 50cm. respectively. Two cuboids have to be cut out from the logs wasting minimum Wood. The unused wasted wood has to be utilised by pasting to make a wooden plank. The price of the cuboid is high and that of plank is less. There are two students; Student A and Student B .Student A cut the first log like in pic. (i) i. e. The cross section is in the shape of a rectangle whose length is 40 cms. and breadth 30 cms. Student B cut the log like in pic. (ii) i.e. the cross section is in the shape of square whose length is 25√2centimeters. Calculate the volume of the cuboids and the wooden planks in each case and find out whose method ( Student A or Student B) is profitable.
Answers
Step-by-step explanation:
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⇒ 5=1×5=5
⇒ 12=2×2×3=22×3
⇒ 18=2×3×3=2×32
⇒ L.C.M of 5, 12 and 18 = 22×32×5=180
⇒ So our four digit number must be divisible by 180.
⇒ Smallest four digit number = 1000
⇒ So, 1801000=5.55≈6
⇒ Smallest four digit number that is divisible by 180 = 180×6=1080
⇒ We know highest four digit number = 9999
⇒ So, 1809999=55.55≈55
∴ Highest four digit number that is divisible by 180 = 180×55=9900
⇒ So, 1080,1260,....9900 is an AP.
⇒ Here, a1=1080,d=180,an=9900
∴ an=a1+(n−1)d
∴ 9900=1080+(n−1)180
∴ 9900=1080+180
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Answer:
(i) and pic. (ii), the length and diameter of each being 21m. and 50cm. respectively. Two cuboids have to be cut out from the logs wasting minimum Wood. The unused wasted wood has to be utilised by pasting to make a wooden plank. The price of the cuboid is high and that of plank is less. There are two students; Student A and Student B .Student A cut the first log like in pic. (i) i. e. The cross section is in the shape of a rectangle whose length is 40 cms. and breadth 30 cms. Student B cut the log like in pic. (ii) i.e. the cross section is in the shape of square whose length is 25√2centimeters. Calculate the volume of the cuboids and the wooden planks in each case and find out whose method ( Student A or Student B) is profitable.