Advertisements
Advertisements
प्रश्न
A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.
उत्तर
For hemisphere,
Radius, r = 8 cm
We know that,
Volume of hemisphere = `2/3 π"r"^3`, where, r = radius of hemisphere
So, we get,
Volume of given hemisphere = `2/3 xx π xx 8^3`
= `(1024/3)π "cm"^3`
Now,
For the cone that is recast from a hemisphere,
Base radius, r = 6 cm
We also know that,
Volume of cone = `1/3 π"r"^2"h"`, where, r is base radius and h is the height of the cone.
So, we get,
Volume of cone = `1/3 π(6)^2"h"` = 12πh
According to the question, we know that,
The volume remains same, when a body is reformed to another body
Volume of cylinder = Volume of cone
12πh = `(1024π)/3`
h = 28.44 cm
APPEARS IN
संबंधित प्रश्न
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?
The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paise / cm2 is
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm, respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.
Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.
A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
