19. How many cubes of 3cm edge can be cut out of a cube of 18cm edge? 20. A tank is 10m long, 10m wide, and 6m deep. The cost of plastering its walls and bottom at 1.0 Rs per sq. m... 19. How many cubes of 3cm edge can be cut out of a cube of 18cm edge? 20. A tank is 10m long, 10m wide, and 6m deep. The cost of plastering its walls and bottom at 1.0 Rs per sq. m is Rs ...? 21. The ages of X and Y are in the proportion of 6:5 and the total of their ages is 44 years. The proportion of their ages after 8 years will be? 22. Find the value of 2/7 of 105 =? × 90. What is the value of? 23. A man riding his bicycle covers 150 metres in 25 seconds. What is his speed in km per hour? 24. The ratio of men to women at a party is 4:7, which of the following could be the number of people at the party? 25. A, B and C together start a business. B invests 1/6 of the total capital while investments of A and C are equal. If the annual profit on this investment is 33600, find the difference between the profits of B and C?
Understand the Problem
The question is asking for solutions to various mathematical problems, including geometry, algebra, and statistics. Each problem requires applying mathematical concepts to find numerical answers or proportions.
Answer
The number of 3 cm edge cubes that can be cut out of an 18 cm edge cube is \( 216 \).
Answer for screen readers
The number of 3 cm edge cubes that can be cut out of an 18 cm edge cube is ( 216 ).
Steps to Solve
- Calculate the volume of the larger cube
The edge length of the larger cube is 18 cm. The volume $V$ of a cube is calculated as: $$ V = \text{edge}^3 = 18^3 $$
- Calculate the volume of one smaller cube
The edge length of the smaller cubes is 3 cm. The volume of one smaller cube is: $$ v = 3^3 $$
- Determine how many smaller cubes fit into the larger cube
To find the number of smaller cubes that can fit, divide the volume of the larger cube by the volume of one smaller cube: $$ \text{Number of cubes} = \frac{V}{v} $$
- Perform arithmetic calculations
First calculate: $$ V = 18^3 = 5832 $$ and $$ v = 3^3 = 27 $$
Then calculate: $$ \text{Number of cubes} = \frac{5832}{27} $$
- Final calculation
Calculate the result of the division: $$ \text{Number of cubes} = 216 $$
The number of 3 cm edge cubes that can be cut out of an 18 cm edge cube is ( 216 ).
More Information
When computing how many smaller cubes fit into a larger cube, it's essential to first determine the volume of each cube using the formula for the volume of a cube, and then use division to find the count of smaller cubes. This concept is useful in geometry and spatial reasoning.
Tips
- Miscalculating the volume of the cubes: Ensure the calculations for volume ( 18^3 ) and ( 3^3 ) are done accurately.
- Forgetting to divide volumes properly: Always double-check the division to ensure it matches the expected outcome of how many smaller cubes fit.
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