Advertisements
Advertisements
प्रश्न
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.
Advertisements
उत्तर
We have,
the height of the cone = the height of the cylinder = h =2.8 cm and the radius of the base, r = `4.2/2 = 2.1 "cm"`
The slant height of the cone, `l = sqrt(r^2 + h^2)`
`=sqrt(2.1^2 + 2.8^2)`
`= sqrt(4.41 +7.84)`
`=sqrt(12.25)`
= 3.5 cm
Now, the total surface area of the remaining solid = CSA of cylinder + CSA of cone + Area of base
`= 2pirh + pirl + pir^2`
`=pir (2h +l +r)`
`= 22/7 xx2.1xx(2xx2.8xx3.5+2.1)`
`= 22xx0.3xx(5.6+5.6)`
`=6.6xx 11.2`
`= 73.92 "cm"^2`
So, the total surface area of the remaining solid is 73.92 cm2.
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.
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
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 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 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.
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?
The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.
A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 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]`
From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [User `pi22/7`]
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
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?
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.
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?
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)
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 ______.
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.
