Advertisements
Advertisements
प्रश्न
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm \[\times\] 42cm \[\times\] 21 cm.
Advertisements
उत्तर
The dimensions of the solid rectangular lead piece is
\[66 cm \times 42 cm \times 21 cm\].
Diameter of the spherical lead shots = 4.2 cm Let n spherical lead shots be obtained from the rectangular piece.
\[n \times\text { volume of spherical lead shot = Volume of the rectangular lead piece}\]
\[ \Rightarrow \frac{\text { Volume of the rectangular lead piece}}{\text { volume of spherical lead shot}} = n\]
\[ \Rightarrow \frac{66 \times 42 \times 21}{\frac{4}{3} \pi r^3} = n\]
\[ \Rightarrow \frac{66 \times 42 \times 21}{\mathit{\frac{4}{3}\pi \left( \frac{4 . 2}{2} \right)^3}} = n\]
\[ \Rightarrow \frac{58212}{38 . 808} = n\]
\[ \Rightarrow n = 1500\]
Hence, 1500 lead shots can be formed.
DISCLAIMER: There is some error in the question given. Instead of 6 cm, there should be 66 cm.
The result obtained is by taking 66 cm as the dimensions of the rectangular piece.
APPEARS IN
संबंधित प्रश्न
If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]
A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 `5/6` cm3. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm2 .[Use`pi=22/7`]
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.
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)
Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?
In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.\[[Use\pi = 3 . 14]\]
A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. `[\text{Use}pi=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.
Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2 .
Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
In a right circular cone, the cross-section made by a plane parallel to the base is a
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.
Ramesh made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
There are two identical solid cubical boxes of side 7 cm. From the top face of the first cube a hemisphere of diameter equal to the side of the cube is scooped out. This hemisphere is inverted and placed on the top of the second cube’s surface to form a dome. Find
- the ratio of the total surface area of the two new solids formed
- volume of each new solid formed.
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.
Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.
500 ml milk is packed in a cuboidal container of dimensions 15 cm × 8 cm × 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm × 32 cm × 15 cm.
Based on the above-given information, answer the following questions:
i. Find the volume of the cuboidal carton. (1)
ii. a. Find the total surface area of the milk packet. (2)
OR
b. How many milk packets can be filled in a carton? (2)
iii. How much milk can the cup (as shown in the figure) hold? (1)
