Calculate 62864

The block volume is 1440 cm³, its surface is 792 cm², and the area of one of its walls is 92 cm². Calculate the lengths of its sides.

Correct answer:

a = 15.6522 cm
b = 11.2296 cm
c = 8.1927 cm

Step-by-step explanation:

V = 1440 cm^{3} S = 792 cm^{3} S_{1} = 92 cm^{2} S_{1} = b c V = a b c a = V / S_{1} = 1440 / 92 = 15.6522 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) 1440 / 15.652173913043 = b ((792 / 2 - 92) / 15.652173913043 - b) b^{2} - 19.422 b + 92 = 0 p = 1; q = - 19.422; r = 92 D = q^{2} - 4 p r = 19.42 2^{2} - 4 \cdot 1 \cdot 92 = 9.2227160494 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 9 . 4 2 \pm 9 . 2 2}{2} b_{1, 2} = 9.711111 \pm 1.518446 b_{1} = 11.229557361 b_{2} = 8.192664862 b = b_{1} = 11.2296 = 11.2296 cm

Our quadratic equation calculator calculates it.

c = (S / 2 - S_{1}) / a - b = (792 / 2 - 92) / 15.6522 - 11.2296 ≐ 8.1927 cm V_{1} = a \cdot b \cdot c = 15.6522 \cdot 11.2296 \cdot 8.1927 = 1440 cm^{3} V_{1} = V S_{2} = 2 \cdot (a \cdot b + b \cdot c + c \cdot a) = 2 \cdot (15.6522 \cdot 11.2296 + 11.2296 \cdot 8.1927 + 8.1927 \cdot 15.6522) = 792 cm^{2} S_{2} = S c = 8.1927 ≐ 8.1927 Verifying Solution: S_{2} = 2 \cdot (a \cdot b + b \cdot c + c \cdot a) = 2 \cdot (15.6522 \cdot 11.2296 + 11.2296 \cdot 8.1927 + 8.1927 \cdot 15.6522) = 792 cm^{2} V_{2} = a \cdot b \cdot c = 15.6522 \cdot 11.2296 \cdot 8.1927 = 1440 cm^{3} S_{3} = b \cdot c = 11.2296 \cdot 8.1927 = 92 cm^{2}

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high school

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