Advertisements
Advertisements
प्रश्न
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`]
Advertisements
उत्तर
Let h be the height of the cone and r be the radius of the base of cone.
The volume of the wooden toy = `1/3pir^2h+2/3pir^3`
`=1/3pir^2(h+2r)`
`=1/3xx22/7xx3.5xx3.5(h+7)`
`=77/6(h+7)`
According to the question,
`77/6(h+7)=166`
`=>77/6(h+7)=1001/6`
⇒h=6
The height of the wooden toy = 6 cm + 3.5 cm = 9.5 cm
Now,
Curved surface area of the hemispherical part = `2xx22/7xx3.5xx3.5 = 77 cm^2`
Hence, the cost of painting the hemispherical part of the toy = 77×10 = Rs 770
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]
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]
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)`
In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use
`pi=22/7`]
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
The internal and external diameters of a hollow hemisphere vessel are 21cm and 25.2 cm The cost of painting 1cm2 of the surface is 10paise. Find total cost to paint the vessel all
over______?
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.\[[Use\pi = 3 . 14]\]
Find the number of metallic circular discs with a 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.
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.
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in level of water in the tank in half an hour.
Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.
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)
Two cubes each of volume 8 cm³ are joined end to end, then the surface area of the resulting cuboid is ______.
Eight solid sphere of same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. The diameter of each sphere is ______.
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
The ratio of total surface area of a solid hemisphere to the square of its radius is ______.
