Take a square sheet of paper of side 10 cm. Four small square are to be cut from the corners if the square sheet and then the paper folded at the cuts to form an open box. What should cut so that the volume of the open box is maximum.
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- -. =(10–2)=2(5-)
, ()=(10–2)^2 =4(5-)^2
(/), ’()=0
=> 4(2*(5–)(-1)+4(5–)^2)=0 => 4(5–)(-2+5–)=0 => 4(5-)(5–3)=0 => ={5, 5/3}. 5 (10–2)=0. =5/3 . 10–2=10–10/3=20/3. ’’()=4(5-)(-2)+4(5–3)(-1)=4(2-10+3–5)=4(5-15)=20(-3)
’’(5/3)=20(5/3–3)=-80/3<0. .
, 20/3()20/3()5/3()
.
MARK ME AS A BRAINLIEST
, ()=(10–2)^2 =4(5-)^2
(/), ’()=0
=> 4(2*(5–)(-1)+4(5–)^2)=0 => 4(5–)(-2+5–)=0 => 4(5-)(5–3)=0 => ={5, 5/3}. 5 (10–2)=0. =5/3 . 10–2=10–10/3=20/3. ’’()=4(5-)(-2)+4(5–3)(-1)=4(2-10+3–5)=4(5-15)=20(-3)
’’(5/3)=20(5/3–3)=-80/3<0. .
, 20/3()20/3()5/3()
.
MARK ME AS A BRAINLIEST
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For the volume of the open box to be maximum, the shape should be cube.
Size of paper = 10cm
Area = 100cm²
since the square should be 9 parts to make open cube and from that, 4 needs to be cut
Dividing by 9 = (100/9)cm²
Total area to be cut = 4 × (100/9) cm²
. = (400/9) cm²
Hence, a total of (400/9) cm, each (100/9) cm is to be cut
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