A volume of 10936 l water is in a container of sphere.How many semisph...
vol.of small container (semi sphere)=4 l
total vol.of water =10936 l
no of small containers required = 10936/4=2734
View all questions of this testA volume of 10936 l water is in a container of sphere.How many semisph...
Given information:
- Volume of water in the container = 10936 liters
- Volume of each small semisphere = 4 liters
To find:
- Number of small semispheres required to transfer all the water
Let's solve the problem step by step:
Step 1: Conversion of units
- 1 liter = 1000 cubic centimeters (cc)
- Volume of water in the container = 10936 liters = 10936 * 1000 cc = 10936000 cc
- Volume of each small semisphere = 4 liters = 4 * 1000 cc = 4000 cc
Step 2: Calculation of the number of small semispheres required
- We know that the volume of a sphere can be calculated using the formula: V = (4/3) * π * r^3
- Since we have small semispheres, we need to consider the volume of a semisphere which is half of the volume of a sphere.
- The volume of a semisphere can be calculated using the formula: V = (2/3) * π * r^3
Let's assume the radius of each small semisphere is 'r' cm.
- Volume of each small semisphere = (2/3) * π * r^3 = 4000 cc
Step 3: Calculation of the number of small semispheres
- We can rearrange the formula to find the radius 'r' as follows: r = (3 * (4000 / π))^(1/3)
- Substituting the value of 'r' in the volume formula, we can calculate the number of small semispheres required.
Let's calculate the number of small semispheres:
r = (3 * (4000 / π))^(1/3)
r ≈ 14.23 cm
Volume of water in the container = Volume of small semispheres
10936000 cc = Number of small semispheres * Volume of each small semisphere
Number of small semispheres = 10936000 cc / 4000 cc
Number of small semispheres ≈ 2734
Therefore, the correct answer is option C) 2734.