Surface area and Volumes
RD Sharma new - Class 10th
- Right circular cylinder with hemisphere on one end and cone on other. Find the surface area of the figure if the radius, height of the cylinder and radius of hemisphere and cone are given
- Cylinder tub with radius and length, circular cone mounted on hemisphere immersed inside. Find the volume of water left
- Cylinder with hemisphere ends. Find the cost of polishing the surface, rupees 10 per dm². Dimensions given in cm - find the surface area in cm then divide by 100.
- Hollow hemisphere mounted on hollow cylinder. Diameter and total height is given. Find the inner surface area of the vessel.
- Cone mounted on hemisphere
- Hemispherical depression is cut out from one face of a cubical wooden block of edge 21cm, such that diameter of hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block
- volume = volume of cube - volume of hemisphere
- total surface area = surface area of the block - area of the base of hemisphere + curved surface area of the hemisphere
- The largest possible sphere is carved out of a wooden solid cube of side 7cm. Find the volume of the wood left
- side = radius
- volume of wood left = volume of cube - volume of sphere
- From a solid cylinder height, a conical cavity of same height and same diameter is hollowed out. Find the total surface area of the remaining solid
- total surface area of remaining solid = csa of cylinder + area of cylindrical base + csa of conical part
- Hemisphere surmounted on a cone, then find volume. If cube circumscribes the shape, find the difference between volume of cube and toy. Find the total surface area of the toy
- volume of cube = side³ = diameter of the shape
- A cone of maximum size of carved out from the cube. Find the surface area of the cone and the remaining solid left out after the cone carved out
- solid remaining = surface area of the cube - area of the cube + curved surface area of the cone
- Marbles of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm. Find the number of marbles that should be dropped into the vessel soo that the water level rises by 5.6 cm
- volume of each marble
- volume of cylinder
- height of the vessel = rise in water level = 5.6 cm
- number of marbles = volume of cylinder / volume of spherical marble
- The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe
- outer surface area - inner surface area = 44
- ie. R - r = 1/2
- outer volume - inner volume = 99
- ie. R + r = 9/2
- find R and r
- Cylinder surmounted by a hemisphere and contains air 41 19/21 m³. Find the height if the internal diameter is equal to the height of the structure.
