Question
Two right circular cones of equal height of radius of
base 3cm and 4cm are melted together and made into a solid sphere of radius 5 cm. The height of the cone is.Solution
Let the radius of two cones r1 and r2. Volume of cones = 1/3× πr2h The volume of two cones = volume of a sphere 1/3× πr12 h +1/3× πr22 h = (4/3) π ×r3 π/3×9h +π/3×16h = 4π/3 ×125 π/3[9h+16h] =4π/3 ×125 25h = 4×125 h=20cm
- The average marks of Priya in 8 subjects was mentioned as 59. Her marks in English and Biology were wrongly recorded as 61 and 48, whereas they should have...
The combined average weight of 8 apples and 5 oranges is 150 grams. If the average weight of the apples is 180 grams, what is the average weight of the ...
Average weight of a team of 16 persons is 37 kg. When one more person joins the team, the average weight of the team increases by 4 kg. Find the weight ...
The average marks of 30 students in Class I is 60. The average marks of some students in Class II is 75. When all students of both classes are taken tog...
- Average of first 2 numbers is twice the average of next 4 numbers. If the average of all 6 numbers is 18, find the sum of the last 4 numbers.
A set contains ten numbers. The average of the first six numbers is (x − 4), and the average of the last three numbers is (x + 2). The average of the...
- The mean of 15 observations is 124 and the median of the observations is 130. Find the mode of the observations.
 A hollow spherical metallic ball has an external diameter 8cm and is 1/2cm thick. The volume of the ball (in cm cube) is.
- The batsman has an average of 32 in 50 innings. His scores in the next 5 innings are 40, 30, 35, 45, and 50. Find his new batting average.
- There are three distinct numbers ‘x’, ‘y’ and ‘z’. If, x = 180, (x + y) = 480 and (z – y) = 60, then find the average of x, y and z.
