Study HubHubPage 135/182Scan verified MCQs with the answer highlighted, then open explanations when you want the reasoning.
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Cuboid Diagonal
The edges of a cuboid are respectively 3 cm, 4 cm, and 12 cm. Find the length of the diagonal of the cuboid.
The length of the diagonal of a cuboid with edges 3 cm, 4 cm, and 12 cm is found using the formula cm. Therefore, the correct answer is 13 cm, which corresponds to option C, not B.
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Cuboid Volume
The edges of a cuboid are 4 cm, 5 cm, and 6 cm. Find the volume of the cuboid.
The volume of a cuboid is calculated by multiplying its length, width, and height. Here, 4 cm × 5 cm × 6 cm = 120 cm³, so the correct answer is 120 cm³.
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Fractions
Which of the following fractions is the largest?
7/8 equals 0.875, which is larger than 13/16 (0.8125), 31/40 (0.775), and 63/80 (0.7875). Therefore, 7/8 is the largest fraction among the options.
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Spheres (Volume)
The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes.
The volume of a sphere is proportional to the cube of its radius. Given the ratio of radii is 1:3, the ratio of volumes is 1³:3³ = 1:27.
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Cubes (Ratio)
If the volumes of two cubes are in the ratio 8:1, what is the ratio of their edges?
The volume of a cube is proportional to the cube of its edge length. Given the volume ratio is 8:1, the edge length ratio is the cube root of 8:1, which is 2:1.
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Box Packing
If in a box of dimensions 6 m × 5 m × 4 m, smaller boxes of dimensions 60 cm × 50 cm × 40 cm are kept in it, then what will be the maximum number of small boxes that can be kept in it?
First, convert the dimensions of the large box to centimeters: 6 m = 600 cm, 5 m = 500 cm, and 4 m = 400 cm. Then, divide each dimension by the corresponding small box dimension: 600/60 = 10, 500/50 = 10, and 400/40 = 10. Multiplying these gives 10 * 10 * 10 = 1000 small boxes that can fit inside the large box.
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Cylinder Surface Area
The radius of a cylindrical vessel is 7 cm and its height is 3 cm. Find the total surface area of the cylinder.
The total surface area (TSA) of a cylinder is calculated using the formula TSA = 2πr(r + h), where r is the radius and h is the height. Given r = 7 cm and h = 3 cm, substituting these values gives TSA = 2 × π × 7 × (7 + 3) = 2 × π × 7 × 10 = 140π ≈ 439.6 sq cm. Among the options provided, 440 sq cm (option C) is the closest to the calculated value. Therefore, the correct answer is C.
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Cubes (Volume)
Three cubes of metal whose edges are 9 cm, 12 cm, and 15 cm respectively, are melted and one new cube is made. Find the edge length of the new cube.
The volumes of the three cubes are calculated as 9³ = 729 cm³, 12³ = 1728 cm³, and 15³ = 3375 cm³. Adding these volumes gives a total volume of 729 + 1728 + 3375 = 5832 cm³. When these three cubes are melted and recast into one cube, the volume of the new cube is 5832 cm³. The edge length of the new cube is the cube root of 5832, which is exactly 18 cm. Therefore, the correct answer is option D (18 cm).
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Hcf And Lcm
Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are___________?
The numbers are in the ratio 1:2:3, so let the numbers be 12x, 24x, and 36x. Since their H.C.F is 12, the common factor x must be 1. Therefore, the numbers are 12, 24, and 36.
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Surface Area & Cost
A room is 15 m long, 4 m broad, and 3 m high. Find the cost of whitewashing its four walls at 50 paise per m².
The area of the four walls of a rectangular room is calculated using the formula: Area = 2 × height × (length + breadth). Here, length = 15 m, breadth = 4 m, and height = 3 m. So, the area = 2 × 3 × (15 + 4) = 2 × 3 × 19 = 114 m². The cost of whitewashing is given as 50 paise per m², which is Rs. 0.5 per m². Therefore, the total cost = 114 × 0.5 = Rs. 57. Hence, the correct answer is Rs. 57, which corresponds to option B.