Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Radius of hemispherical ends = radius of cylinder
`=1/2 xx 0.7`
`=7/20 m`
Total length = 2.7 m.
Height of cylinder
`=2.7 - 2 xx 7/20`
`= 2m`
Volume of two hemispheres
`=2 (2/3 pir^3)`
`=4/3 pir^3`
`=4/3 xx 22/7 xx (7/20)^3`
`=4/3 xx 22 /7 xx (343)/(800)`
` = 0.1797 m^3`
Volume of cylinders
` =pir^2h`
`=22/7 xx (7/20)^2 xx 2`
`=0.77 m^2`
Hence,
Volume of solid = 0.1797+0.77 = 0.95 m3
APPEARS IN
संबंधित प्रश्न
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs. 5 per 100 sq. cm. [Use π = 3.14]
In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use `pi=22/7` and `sqrt5=2.236`)
A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π =`22/7`)
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm3. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of Rs 1.4 per cm2?
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.
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.
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
A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases is ______.
Two cubes each of volume 8 cm³ are joined end to end, then the surface area of the resulting cuboid is ______.
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is `pir [sqrt(r^2 + h^2) + 3r + 2h]`.
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.
3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid.
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)
