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Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
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Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.
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The shape of a gilli in the gilli-danda game is a combination of ______.
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A plumbline (sahul) is the combination of ______.
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In a right circular cone, the cross-section made by a plane parallel to the base is a ______.
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If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is ______.
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The volume of a hemisphere is 19404 cm3. The total surface area of the hemisphere is ______.
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Match the following columns:
| Column I | Column II |
| (a) The radii of the circular ends of a bucket, in the form of the frustum of a cone of height 30 cm, are 20 cm and 10 cm respectively. The capacity of the bucket is ........cm3. `["Take" π = 22/7`.] |
(p) 2418π |
| (b) The radii of the circular ends of a conical bucket of height 15 cm are 20 and 12 cm respectively. The slant height of the bucket is ........ cm. |
(q) 22000 |
| (c) The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is .........cm2. |
(r) 12 |
| (d) Three solid metallic spheres of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is ........ cm. |
(s) 17 |
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A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3. The radii of the top and bottom of the circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it. (Use π = 3.14)
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A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
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A container opened at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm2. (Take π = 3⋅14)
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sin (45° + θ) – cos (45° – θ) is equal to ______.
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If `sqrt2 sin (60° – α) = 1` then α is ______.
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The value of sin² 30° – cos² 30° is ______.
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If cos (40° + A) = sin 30°, then value of A is ______.
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If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
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`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
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If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
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If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.
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3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to ______.
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