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प्रश्न
A metallic sheet is of the rectangular shape with dimensions 48cm x 36cm. From each one of its corners, a square of 8cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box.
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उत्तर
Given that
Dimensions of metallic sheet:
Length (l) = 48cm
Breadth (b) = 36cm
Side (S) of each square = 8cm.
Now,
Area of metallic sheet
= l x b
= 48 x 36
= 1728cm2
Area of 1 square
= S x S
= 8 x 8
= 64cm2
∴ Area of 4 square
= 64 x 4
= 256cm2
Thus, remaining area in the sheet after reducing the area of 4 squares:
Remaining area
= 1728 - 256
= 1472cm2 ................................(1)
Since 8cm square is cut off from all sides, we get the dimensions of open box as:
Length (l) = 48 - 16 = 32cm
Breadth (b) = 36 - 16 = 20cm
Area of the box = L.S.A of the box + area of base of the box
1472 = {2 x h x (l + b)} + (l x b) ...[From (1)]
1472 = {2 x h x (32 + 20)} + (32 x 20)
1472 = {2h x 52} + 640
1472 = 104h + 640
104h = 1472 - 640
h = `(832)/(104)`
i.e., height(h) = 8cm
Thus,
volume of the box
= l x b x h
= 32 x 20 x 8
= 5120cm3.
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