Question
A right circular cylinder having total surface area of
44352 cm2 is immersed in a vessel completely filled with water. If the height of the cylinder is 25% more than its radius, what is the amount of water displaced (in cm3)?Solution
Let the radius and height of the cylinder be r and h cm respectively. ∴ h = 1.25r Total surface area of the cylinder = 44352 = 2πr(h + r) ∴ 44352 = 2πr(1.25r + r) = 2πr(2.25r) = 4.5πr2 ∴ 44352 = (9/2) × (22/7) × r2 = 44352 x 7 x 2/22 x 9 ∴ r2 = 3136 ∴ r = 56 and h = 70 Amount of water displaced = Volume of the right circular cylinder = πr2h = (22/7) × (56)2 × (70) = 689920 cm³
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 40x + 300 = 0
Equation 2: y² - 30y + 216 = 0
(i) 2x² + 14x - 16 = 0
(ii) y² – y – 12 = 0
I. x² - (16)2 = 0
II. 2y - 14 = 0
If the roots of the quadratic equation 6m² + 7m + 8 = 0 are α and β, then what is the value of [(1/α) + (1/β)]?
I. 15b2 + 26b + 8 = 0
II. 20a2 + 7a - 6 = 0
Find the remainder when x⁵ − 3x⁴ + 4x³ − 6x² + 8x − 3 is divided by (x − 2).
I. 3p2 - 11p + 10 = 0
II. 42q2 + q -1 = 0
I. x2 – 13x + 40 = 0
II. 2y2 – 15y + 13 = 0
I: 2x² - 8x + 6 = 0
II: 3y² - 12y + 9 = 0
Solve the given two equations and answer the two questions that follow as per the instructions given below.
I. (1/4) + 7.5p(-2) = 3.62...
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