A sphere has radius 3 cm. Find its volume in $cm^3$. (Take pi = 22/7)
Volume = (4/3) * pi * $r^3$ = (4/3) * (22/7) * 27 = 36 * (22/7) = 113.14 $cm^3$.
By selling 33 meters of cloth, a person gains the cost price of 11 meters. Find the gain percentage.
Gain = CP of 11m. Gain % = (Gain / CP of 33m) * 100 = (11 / 33) * 100 = 33.33%.
Solve for x: $3^(x+2) + 3^x$ = 90
$3^x$ $(3^2 + 1)$ = 90 => $3^x$ (10) = 90 => $3^x$ = 9 => x = 2.
The perimeter of a rectangular field is 80 meters and its length is 24 meters. Find its breadth.
Perimeter = 2(l + b) => 80 = 2(24 + b) => 40 = 24 + b => b = 16 meters.
Two dice are thrown simultaneously. What is the probability of getting a sum of 8?
Favorable outcomes for sum 8: (2,6), (3,5), (4,4), (5,3), (6,2) -> 5 outcomes out of 36 total.