The ratio of the heights of a right circular cone and a right circular cylinder is 2 : 9 and the ratio of the radii of their bases is 7 : 2. If the volume of the cylinder is 972 cm³ , then the volume (in cm³ ) of the cone is:
Given:
Ratio of height of cone () to cylinder () = 2 : 9
Ratio of radius of cone () to cylinder () = 7 : 2
Volume of cylinder = 972 cm³
Formula Used:
Volume of cylinder =
Volume of cone =
Solution:
Let = 2h and = 9h.
Let = 7r and = 2r.
Volume of cylinder =
It is given that
Volume of cone =
Volume of cone =
Substitute the value of :
Volume of cone =
Volume of cone = 98 × 9 = 882 cm³
Final Answer
So the correct answer is (d)
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A metal sphere of radius 36 cm is immersed in a cylindrical vessel that is partially filled with water. The diameter of the vessel is 4.8 m. If the sphere is completely submerged in the water, find the rise in the water level.
The ratio of the heights of a right circular cone and a right circular cylinder is 2 : 9 and the ratio of the radii of their bases is 7 : 2. If the volume of the cylinder is 972 cm³ , then the volume (in cm³ ) of the cone is:
A solid is in the shape of a cone mounted on a hemisphere. The radius of each is 6 cm and the total height of the solid is 14 cm . Find the surface area of the solid.
The curved surface area of a solid metallic right circular cylinder is 1792π cm² and its base radius is 32 cm. It is melted and recast into 42 solid spherical balls of equal radius. What is the surface area (in cm²) of a ball ?
The number of bricks, which will be required to make a wall which is 8m long, 6m high and 22.5 cm thick if each brick measures 25 cm ×11.25 cm × 6 cm is
A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The contents ofthe vessel are emptied into a cylindrical vessel with base of internal radius 15 cm. The height (in cm) to which the liquid will rise in the cylindrical vessel is:
The diameter of a solid metallic sphere is 3.5 cm. Such 96 spheres are melted and recast into a solid right circular cylinder of height 56 cm.
What is the curved surface area (in cm²) of the cylinder?
A solid hemisphere of radius 10 cm is melted into two cones of equal height. If each cone’s radius is 5 cm, what is the height of each cone?
A hemisphere and a cone share the same base and have equal volumes. Given that their common radius is R, determine the height of the cone.
Suggested Test Series
Suggested Test Series
A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm . The number of such cones is :
A metal sphere of radius 36 cm is immersed in a cylindrical vessel that is partially filled with water. The diameter of the vessel is 4.8 m. If the sphere is completely submerged in the water, find the rise in the water level.
The ratio of the heights of a right circular cone and a right circular cylinder is 2 : 9 and the ratio of the radii of their bases is 7 : 2. If the volume of the cylinder is 972 cm³ , then the volume (in cm³ ) of the cone is:
A solid is in the shape of a cone mounted on a hemisphere. The radius of each is 6 cm and the total height of the solid is 14 cm . Find the surface area of the solid.
The curved surface area of a solid metallic right circular cylinder is 1792π cm² and its base radius is 32 cm. It is melted and recast into 42 solid spherical balls of equal radius. What is the surface area (in cm²) of a ball ?
The number of bricks, which will be required to make a wall which is 8m long, 6m high and 22.5 cm thick if each brick measures 25 cm ×11.25 cm × 6 cm is
A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The contents ofthe vessel are emptied into a cylindrical vessel with base of internal radius 15 cm. The height (in cm) to which the liquid will rise in the cylindrical vessel is:
The diameter of a solid metallic sphere is 3.5 cm. Such 96 spheres are melted and recast into a solid right circular cylinder of height 56 cm.
What is the curved surface area (in cm²) of the cylinder?
A solid hemisphere of radius 10 cm is melted into two cones of equal height. If each cone’s radius is 5 cm, what is the height of each cone?
A hemisphere and a cone share the same base and have equal volumes. Given that their common radius is R, determine the height of the cone.
