For a cube of side a, volume is V = a³, giving a = V¹ᐟ³. Since total surface area is S = 6a², substituting a yields S = 6V²ᐟ³ or 6∛(V²). Class 9 Ganita Manjari part 2 Chapter 14 end of ...
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(i) Option (c): New volume (l + 1)wh minus original lwh gives wh cubic units. (ii) Option (e): π(r + 1)²h − πr²h = 2πrh + πh cubic units. (iii) Volume decreases by (4/3)π(3r² − 3r + 1) cubic units. Ganita Manjari Part ...
Let the father’s age be F, which equals children’s sum S. In 20 years, children gain 4 × 20 = 80 years: F + 80 = 2(F + 20). This gives F + 80 = 2F + 40, so F ...
Let speed be s and time t. The conditions give (s + 6)(t − 6) = st and (s − 4)(t + 6) = st, simplifying to t − s = 6 and 3s − 2t = 12. Solving yields ...
Opposite angles sum to 180°, giving x + 3y = 150 and 4x + y = 160. Solving gives x = 30 and y = 40. The angles are ∠A = 37°, ∠B = 48°, ∠C = 143° and ∠D ...