Question
A frustum of a cone has a lower base radius of 12 cm, an
upper base radius of 8 cm, and a height of 15 cm. Find the total surface area of the frustum.Solution
The slant height (l) of the frustum is given by l = √(h² + (r1 - r2)²), where h = 15 cm, r1 = 12 cm, and r2 = 8 cm. Slant height l = √(15² + (12 - 8)²) = √(225 + 16) = √241 ≈ 15.52 cm. The total surface area of the frustum = π * (r1 + r2) * l + π * (r1² + r2²). Total surface area = π * (12 + 8) * 15.52 + π * (12² + 8²). = π * 20 * 15.52 + π * (144 + 64). = 310.4π + 208π = 518.4π square cm.
- The probability that Ankit passes is (2/9) and the probability that Shruti fails is (7/13). Find the probability that both have the same result.
A box contains 5 blue jellies, some red jelly and rest yellow jelly. The probability of picking a red ball at random is 3/10, while the probability of p...
The chance that Nikhil can solve a certain problem is1/7, the chance that Tarun can solve it is3/5. Find the probability that the problem is solved if t...
A game consists of tossing three coins once and then rolling two dice. Find the probability of getting exactly two heads in the coin toss and a sum equa...
A box has ‘x’ blue balls and 9 yellow balls. If the probability of selecting a blue ball is 3/7, then find the probability of drawing two balls of d...
A box contains 4 red, 5 blue and 3 green balls. Two balls are drawn at random without replacement. Find the probability that both balls are of the same ...
- A bag contains ‘x’ white balls and 3 black balls. If the probability of getting a white ball is 4/5, then find the probability of getting different col...
What will be the probability of choosing one red and one green ball from a basket containing 4 red and 5 green balls if two balls are drawn randomly?
In how many ways can the letters of the word "COMPUTER" be arranged, and what is the probability that all the vowels in these arrangements always appear...
A bag contains (2x + y) red balls, 32 black balls, and (3x – y) yellow balls. The probability of drawing a red ball is 4/13, and the probability of dr...
