Calculate 7653

The block volume is 900 cm³, and the surface is 600 cm². The area of one wall is 60 cm². Calculate the length of edges a, b, and c.

Correct answer:

a = 15 cm
b = 10 cm
c = 6 cm

V = 900 cm^{3} S = 600 cm^{3} S_{1} = 60 cm^{2} S_{1} = b c V = a b c a = V / S_{1} = 900 / 60 = 15 cm

S = 2 (a b + b c + c a) = 2 (a b + S_{1} + c a) S / 2 - S_{1} = a b + c a b + c = (S / 2 - S_{1}) / a V / a = b c = b ((S / 2 - S_{1}) / a - b) V / a = b ((S / 2 - S_{1}) / a - b) 900 / 15 = b ((600 / 2 - 60) / 15 - b) b^{2} - 16 b + 60 = 0 p = 1; q = - 16; r = 60 D = q^{2} - 4 p r = 1 6^{2} - 4 \cdot 1 \cdot 60 = 16 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 6 \pm 1 6}{2} b_{1, 2} = \frac{1 6 \pm 4}{2} b_{1, 2} = 8 \pm 2 b_{1} = 10 b_{2} = 6 b = b_{1} = 10 = 10 cm

c = (S / 2 - S_{1}) / a - b = (600 / 2 - 60) / 15 - 10 = 6 V_{1} = a \cdot b \cdot c = 15 \cdot 10 \cdot 6 = 900 cm^{3} V_{1} = V S_{2} = 2 \cdot (a \cdot b + b \cdot c + c \cdot a) = 2 \cdot (15 \cdot 10 + 10 \cdot 6 + 6 \cdot 15) = 600 cm^{2} S_{2} = S c = 6 = 6 cm

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