Chapter 7 Mensuration Class 10 Maharashtra Board TextBook Solution
Practice set 7.1 | Q 6 | Page 145
Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?
Answer:-
The problem provides the following information:
- Radius of the conical water jug, r = 3.5 cm
- Height of conical water jug, h = 10 cm
- Radius of cylindrical pot, R = 7 cm
- Height of cylindrical pot, H = 10 cm
The code calculates the number of conical water jugs that the cylindrical pot can hold. This is done using the formula:
n = Volume of cylindrical water pot / Volume of conical water jug
The volume of a cylinder is given by the formula: V = πr^2h, where r is the radius and h is the height. The volume of a cone is given by the formula: V = (1/3)πr^2h, where r is the radius and h is the height.
Substituting the given values, we get:
n = (πR^2H) / [(1/3)πr^2h]
Simplifying this equation, we get:
n = (3R^2H) / (r^2h)
Substituting the given values, we get:
n = (3 * 7^2 * 10) / (3.5^2 * 10)
Simplifying this equation, we get:
n = 12
Therefore, the cylindrical water pot can hold water of 12 conical water jugs.
Solution
The Radius of the conical water jug, r = 3.5 cm
Height of conical water jug, h = 10 cm
the radius of a cylindrical pot, R = 7 cm
Height of cylindrical pot, H = 10 cm
Let n be the number of jugs of water that cylindrical pot can hold.
[therefore n = frac{text{ Volume of cylindrical water pot} }{text{ Volume of conical water jug} }]
[ Rightarrow n = frac{pi R^2 H}{frac{1}{3}pi r^2 h}]
[ Rightarrow n = frac{3 times left( 7 right)^2 times 10}{left( 3 . 5 right)^2 times 10} = 12]
Thus, the cylindrical water pot can hold water of 12 conical water jugs.
Chapter 7 Mensuration Textbook Solution 7.1
Practice set 7.1
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