Advertisements
Advertisements
प्रश्न
The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:
विकल्प
3
5
4
6
Advertisements
उत्तर
Let r and h be the radius and the height of the cylinder, respectively.
Given:
Diameter of the cylinder = 4 cm
∴ Radius of the cylinder, r = 2 cm
Height of the cylinder, h = 45 cm
Volume of the solid cylinder = `pir^2h=pixx(2)^2xx45 cm^2=180pi cm^3`
Suppose the radius of each sphere be R cm.
Diameter of the sphere = 6 cm
∴ Radius of the sphere, R = 3 cm
Let n be the number of solids formed by melting the solid metallic cylinder.
∴ n × Volume of the solid spheres = Volume of the solid cylinder
`=>nxx4/3 pi R^3=180pi`
`=>nxx4/3 pi(3)^3=180pi`
`=>n=(180xx3)/(4xx27)=5`
Thus, the number of solid spheres that can be formed is 5.
Hence, the correct option is B.
APPEARS IN
संबंधित प्रश्न
Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pay. What values are shown by these associations? [Use π=22/7]
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. `("use " pi=22/7)`
A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. (use π 3.14).
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2
[use `pi = 22/7`]
Find the area of the shaded region in Fig. 3, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]
A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)
The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.
A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.
A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.
In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm ?
The shape of the gilli used in a gilli-danda game is a combination of
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
The total surface area of a solid hemisphere of radius 7 cm is ______.
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
