Theory question 108
Mensuration of Solids(a) An open rectangular tank is made of a steel plate of area 1440m2. Its length is twice its width. If the depth of the tank is 4m less than its width, find its length.
(b) A man saved N3,000 in a bank P, whose interest rate was x% p.a. and N2,000 in another bank Q whose interest rate was y% p.a. His total interest in one year was N640. If he had saved N2,000 in P and N3,000 in Q for the same period, he would have gained N20 as additional interest. Find the values of x and y.
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(a) Width b, length 2b, depth b − 4. Open top: base + four sides = 2b2 + 2(2b)(b − 4) + 2b(b − 4) = 8b2 − 24b = 1440.
b2 − 3b − 180 = 0, (b − 15)(b + 12) = 0, b = 15. Length = 30 m.
(b) 30x + 20y = 640 and 20x + 30y = 660, i.e. 3x + 2y = 64 and 2x + 3y = 66.
Solving: x = 12, y = 14.
An open tank has no top, so count the base and four sides only.