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 Mensuration 30 Flashcards |
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What is mensuration? |
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Mensuration is a branch of mathematics that deals with the measurement of geometric figures and their parameters like length, area, volume, and surface area. |
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How do you calculate the area of a rectangle? |
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The area of a rectangle is calculated by multiplying its length by its width. The formula is Area = Length × Width. |
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What is the formula for the volume of a cylinder? |
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The volume of a cylinder is calculated using the formula Volume = πr²h, where r is the radius of the base and h is the height of the cylinder. |
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If the radius of a circle is doubled, how does it affect the area? |
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If the radius of a circle is doubled, the area increases by a factor of four. This is because the area A = πr²; if r is doubled (2r), the new area is A = π(2r)² = 4πr². |
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Calculate the surface area of a cube with a side length of 3 cm. Hint: Use the formula Surface Area = 6s², where s is the length of a side. |
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Using the formula Surface Area = 6s²: Surface Area = 6(3 cm)² = 6(9 cm²) = 54 cm². |
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What is the area of a circle with a radius of 4 cm? Hint: Use the formula Area = πr². |
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Area = π(4 cm)² = π(16 cm²) = 16π cm². |
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Find the volume of a sphere with a radius of 5 cm. Hint: Use the formula Volume = (4/3)πr³. |
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Volume = (4/3)π(5 cm)³ = (4/3)π(125 cm³) = (500/3)π cm³. |
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What is the formula for the perimeter of a triangle? Hint: The perimeter is the sum of all sides. |
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Perimeter = a + b + c, where a, b, and c are the lengths of the sides of the triangle. |
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How do you find the total surface area of a cylinder? Hint: Total Surface Area = 2πr(h + r). |
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Total Surface Area = 2πr(h + r), where r is the radius and h is the height of the cylinder. |
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Calculate the area of a trapezium with bases 6 cm and 10 cm, and height 4 cm. Hint: Use the formula Area = ½(h(a + b)). |
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Area = ½(4 cm)(6 cm + 10 cm) = ½(4 cm)(16 cm) = 32 cm². |
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What is the lateral surface area of a cone with radius 3 cm and slant height 5 cm? Hint: Use the formula LSA = πrl. |
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LSA = π(3 cm)(5 cm) = 15π cm². |
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Determine the volume of a cuboid with dimensions 4 cm, 5 cm, and 6 cm. Hint: Use the formula Volume = l × b × h. |
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Volume = 4 cm × 5 cm × 6 cm = 120 cm³. |
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What is the area of a scalene triangle with sides 5 cm, 6 cm, and 7 cm? Hint: Use Heron's formula: Area = √[s(s−a)(s−b)(s−c)], where s = (a + b + c)/2. |
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S = (5 + 6 + 7)/2 = 9; Area = √[9(9−5)(9−6)(9−7)] = √[9×4×3×2] = √(216) = 6√6 cm². |
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How do you calculate the area of a rhombus with diagonals 8 cm and 6 cm? Hint: Use the formula Area = ½(d1 × d2). |
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Area = ½(8 cm × 6 cm) = 24 cm². |
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What is the formula for the area of a circle? |
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The area of a circle is calculated using the formula Area = πr², where r is the radius of the circle. |
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Completed! Keep practicing to master all of them. |
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