Advertisements
Advertisements
प्रश्न
The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. Find the diameter of the base of the cone.
उत्तर
Internal radius = 3 cm
External radius = 5 cm
Volume of spherical shell
= `4/3pi(5^3 - 3^3)`
= `4/3 xx 22/7(125 - 27)`
= `4/3 xx 22/7 xx 98`
Volume of solid circular cone
= `1/3pir^2h`
= `1/3 xx 22/7 xx r^2 xx 32`
Vol. of cone = Vol. of sphere
`=> 1/3 xx 22/7 xx r^2 xx 32 = 4/3 xx 22/7 xx 98`
`=> r^2 = (4 xx 98)/32`
∴ `r = 2 xx 7/2`
∴ r = 7 cm
APPEARS IN
संबंधित प्रश्न
Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.
The area of the curved surface of a cone is 60 cm2. If the slant height of the cone be 8 cm, find the radius of the base?
The radius and slant height of a cone are In the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use it 𝜋 = 22/7).
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.
Find the volume of a right circular cone with:
height 21 cm and slant height 28 cm.
Monica has a piece of Canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.
Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitchings. Also, find the cost of the canvas at the rate of Rs. 24 per metre.
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
The radii of the bases of two solid right circular cones of same height are r1 and r2 respectively. The cones are melted and recast into a solid sphere of radius R. Find the height of each cone in terms r1, r2 and R.
A solid, consisting of a right circular cone standing one a hemisphere, is placed upright in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of
the hemisphere is 2 cm and the height of cone is 4 cm. Give your answer to the nearest cubic centimeter.
What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making is Rs.10 per sq.m? `(π = 22/7)`
The curved surface area of a cone is 2200 sq.cm and its slant height is 50 cm. Find the total surface area of cone. `(π = 22/7)`
Find the radius of the circular base of the cone , if its volume is 154 cm3 and the perpendicular height is 12 cm
The radius and height of a cylinder, a cone and a sphere are same. Calculate the ratio of their volumes.
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: total surface area.
The radius and height of cone are in the ratio 3 : 4. If its volume is 301.44 cm3. What is its radius? What is its slant height? (Take π = 3.14)
The circumference of the base of a 10 m high conical tent is 44 metres. Calculate the length of canvas used in making the tent if the width of the canvas is 2m. (Take π = 22/7)
A metallic cylinder has a radius of 3 cm and a height of 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder, as shown and it is completely filled with a lighter metal B. The conical hole has a radius of `3/2` cm and its depth is `8/9` cm. Calculate the ratio of the volume of the metal A to the volume of metal B in the solid.
