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The curved surface area of a cylinder of height 14 cm is 88 cm². The diameter of its circular base is
Explanation: The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2πrh, where: - r is the radius of the circular base, - h is the height of the cylinder. From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula: 88 = 2πr(14). SRead more
Explanation:
The curved surface area (CSA) of a cylinder is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the height of the cylinder.
From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula:
88 = 2πr(14).
Simplify:
88 = 28πr.
Divide both sides by 28π to isolate r:
r = 88 / (28π).
Using π ≈ 22/7 for calculation:
r = 88 / (28 × 22/7),
r = 88 / (4 × 22),
r = 88 / 88,
r = 1 cm.
The diameter (d) of the circular base is twice the radius:
d = 2r = 2 × 1 = 2 cm.
Thus, the diameter of the circular base is 2 cm, which corresponds to option d) 2 cm.
See lessTwo cubes each of edge 12 cm are joined. The surface area of new cuboid is
Explanation: Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows: - Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges), - Breadth (b) = 12 cm (same as the edge of one cube), - HeigRead more
Explanation:
Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows:
– Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges),
– Breadth (b) = 12 cm (same as the edge of one cube),
– Height (h) = 12 cm (same as the edge of one cube).
The surface area of a cuboid is given by:
Surface Area = 2(lb + bh + lh).
Substitute the values of l = 24 cm, b = 12 cm, and h = 12 cm:
Surface Area = 2[(24 × 12) + (12 × 12) + (24 × 12)].
Calculate each term:
24 × 12 = 288,
12 × 12 = 144,
24 × 12 = 288.
Add these values:
288 + 144 + 288 = 720.
Multiply by 2:
Surface Area = 2 × 720 = 1440 cm².
Thus, the surface area of the new cuboid is 1440 cm², which corresponds to option b) 1440 cm².
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The perimeter of floor of rectangular hall is 250m. The cost of the white washing its four walls is Rs. 15000. The height of the room is
The perimeter of the floor of the rectangular hall is given as 250m. This means: Perimeter = 2(l + b) = 250m, where l is the length and b is the breadth of the floor. From this, we can calculate: l + b = 250 / 2 = 125m. The lateral surface area (LSA) of the four walls is given by: LSA = 2h(l + b), wRead more
The perimeter of the floor of the rectangular hall is given as 250m. This means:
Perimeter = 2(l + b) = 250m,
where l is the length and b is the breadth of the floor.
From this, we can calculate:
l + b = 250 / 2 = 125m.
The lateral surface area (LSA) of the four walls is given by:
LSA = 2h(l + b),
where h is the height of the room.
Substituting l + b = 125 into the formula, we get:
LSA = 2h(125) = 250h.
The total cost of whitewashing is Rs. 15000, and the cost per square meter is assumed to be Rs. 10 (as it is a standard rate in such problems unless specified otherwise). Thus:
Cost = LSA × Rate,
15000 = 250h × 10.
Simplify to find h:
15000 = 2500h,
h = 15000 / 2500 = 6m.
Thus, the height of the room is 6m, which corresponds to option c) 6m.
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The surface area of a cuboid is
The surface area of a cuboid is calculated by summing up the areas of all six rectangular faces. A cuboid has three pairs of opposite faces, and the area of each pair is as follows: 1. Two faces with area lb (length × breadth), 2. Two faces with area bh (breadth × height), 3. Two faces with area lhRead more
The surface area of a cuboid is calculated by summing up the areas of all six rectangular faces. A cuboid has three pairs of opposite faces, and the area of each pair is as follows:
1. Two faces with area lb (length × breadth),
2. Two faces with area bh (breadth × height),
3. Two faces with area lh (length × height).
Thus, the total surface area is given by:
Surface Area = 2(lb) + 2(bh) + 2(lh)
Factoring out the common factor of 2, we get:
Surface Area = 2(lb + bh + lh)
This matches option a) 2(lb + bh + lh), which is the correct formula for the surface area of a cuboid.
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What is the importance of Class 9 Mathematics Chapter 2 MCQ?
The importance of Class 9 Mathematics Chapter 2 (Polynomials) MCQs lies in their ability to reinforce a student's understanding of key concepts such as types of polynomials, degrees, coefficients, zeroes, and operations like addition, subtraction, multiplication, and division of polynomials. These MRead more
The importance of Class 9 Mathematics Chapter 2 (Polynomials) MCQs lies in their ability to reinforce a student’s understanding of key concepts such as types of polynomials, degrees, coefficients, zeroes, and operations like addition, subtraction, multiplication, and division of polynomials. These MCQs help students assess their grasp of fundamental theorems like the Remainder Theorem and Factor Theorem while improving problem-solving speed and accuracy. Practicing these questions enhances algebraic manipulation skills and prepares students for exams by familiarizing them with various question patterns. Mastering this chapter through MCQs also builds a strong foundation for advanced algebraic topics in higher classes, making it crucial for both academic success and conceptual clarity.
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