Question
The area of a rhombus is 1,600 cm², and the lengths of its
diagonals are in the ratio 5:4. A circle is constructed with the smaller diagonal as the diameter. Find the difference between the area of the circle and 75% of the rhombus's area. (Take π = 3)Solution
ATQ,
Let diagonals = 5x and 4x
Area = (1/2) × 5x × 4x = 10x²
1600 = 10x² → x² = 160 → x = √160 ≈ 12.65
Smaller diagonal = 4x ≈ 50.6 cm
Radius ≈ 25.3 cm
Area of circle ≈ 3 × (25.3)² ≈ 3 × 640 ≈ 1920 cm²
75% of rhombus = 0.75 × 1600 = 1200 cm²
Difference ≈ 1920 - 1200 = 720 cm²
A 88-litre mixture contains only water and oil in the ratio 6:5, respectively. If 22 litres of the mixture is replaced with the same quantity of oil, th...
Suppose you have 60 litres of milk, which you can purchase at Rs. 35 for every 1.5 litres. How many litres of water should you add to this milk to reduc...
- 150 litres of solution 'C' has milk and water in the ratio 3:2, and 350 litres of solution 'D' has them in the ratio 7:3. Find the final ratio of milk to w...
2 Kg of sugar at Rs 30 per Kg is mixed with 3 Kg of 2nd type of sugar to get a mixture costing Rs 46 per Kg. Find the price of the costlier sugar
Quantity of water in a 420 litres mixture (Milk + Water) is 20 litres less than the quantity of milk in it. Find the quantity of water to be mixed so th...
Mixture ‘X’ contains 50% alcohol and the rest 40 litres of water. 150 litres of mixture ‘Y’ contains alcohol and water in the ratio 5:10, respec...
When 10 litres of water is added to a mixture of milk and water, the ratio of quantity of milk and water becomes 4:5. Instead, if 20 litres of water had...
A mixture has milk and water in ratio 7:3. If 5 liters of water is added, ratio becomes 7:4. Find quantity of milk.
- In a solution, the ratio of milk to water is 4:5. If 6 litres of milk and 12 litres of water are added, the new ratio becomes 5:7. What was the original qu...
A mixture (paint + thinner) contains paint and thinner in the ratio of 9:5, respectively. If 56 litres of the mixture is replaced with 28 litres of thi...
Relevant for Exams:
