Advertisements
Advertisements
प्रश्न
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =`22/7`]
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
उत्तर
Radius of hemisphere = 3.5 cm
total height of the toy = 15.5 cm.
Surface area of cone `=pirl`
`l = sqrt((12)^2 + (3.5)^2)`
`= sqrt156.25`
`=12.5 cm`
Therefore,
Surface area of cone
`= 22/7 xx 3.5 xx 12.5`
`=137.5 cm^2`
Surface area of hemisphere `=2pir^2`
`= 2 xx 22/7 xx 3.5 xx 3.5`
`= 77 cm^2`
Therefore,
Total surface area of the toy
`=137.5 + 77`
`=214.5 cm^2`
Volume of cone
`=1/3pir^2h`
`=1/3 xx 22/7 xx (3.51^2 xx 12)`
`=154 cm^2`
Volume of hemisphere
`=2/3pir^3`
`= 2/3 xx 22/7 xx (3.5)^3`
`= 89.83 cm `
Therefore,
Total volume of the toy
`= (154 + 89.83) cm^3`
`= 243.83 cm^3`
APPEARS IN
संबंधित प्रश्न
A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.
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]
If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]
The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).
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 cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. [Use `pi = 22/7`]
Water in a canal, 5·4 m wide and 1·8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?
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 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)
In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. `[\text\ User=22/7]`
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 .
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
The volume of a hemisphere is 2425 `1/2` cm3 . Find its curved surface area.
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 cubes of 10 cm edge can be put in a cubical box of 1 m edge?
If two solid hemispheres of the same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
A plumbline (sahul) is the combination of (see figure) ______.
|
Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as "The Ceramic Town". One of the private schools of Bulandshahr organised an Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.
Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
Maths teacher who was accompanying the students asked the following questions:
- The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and the radius and height of the cylindrical jar in II are 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?
- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
