The height of a right circular cone is 30 cm. A small cone is cut off from the top by a plane parallel to the base of the cone. If the volume of the small cone is of the volume of the given cone, then at what height above the base was the cone cut?
Let:
H = 30 cm (Height of the original cone)
h = Height of the small cone
V_small / V_large = (h/H)³ = 1/27
(h / 30)³ = 1/27
Step 2: Solving for h
Taking the cube root on both sides:
(h / 30) = 1/3
h = 30 × 1/3 = 10 cm
Thus, the small cone has a height of 10 cm, meaning it was cut at:
Height from the base = 30 - 10 = 20 cm.
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A triangle ABC with sides 3 cm, 4 cm and 5 cm is revolved about the side 3 cm. Find the volume of the solid so obtained. (Use π = 3.14)
If the areas of three adjacent faces of a cuboid are x, y, z square units, respectively, then the volume of the cuboid is:
A cylindrical water tank has a base radius of 7 m and a height of 10 m. Water is filled into the tank at a constant rate. After filling the tank completely, 5% of the water leaks out due to a crack at the bottom. The remaining water is transferred into another cylindrical tank whose base radius is 5 m. Find the height of water in the second tank.
A cube is painted on all faces and then cut into 27 smaller cubes of equal sizes. How many smaller cubes have exactly two faces painted ?
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.
A solid cube of 4 inches has been painted red, green and black on pair of opposite faces. It has been cut into one inch cubes. How many cubes will have only two faces painted?
From a cuboid of dimension 10cm×5cm×2.5cm, small cubes of edge 2.5 cm are cut. How many small cubes are formed from the cuboid?
The total surface area of a hemisphere is 4,158 . If the radius of the hemisphere becomes one-third of itself, then what will be the new curved surface area of the hemisphere? (Use π=22/7 )
If the volume of a cone is 48π and the height is 10 cm . Find the radius of its base in nearest one decimal place.
Suggested Test Series
Suggested Test Series
A square tank holds 15,000 litres of water. If its depth is 2.5 m, find the length of one side of its base.
A triangle ABC with sides 3 cm, 4 cm and 5 cm is revolved about the side 3 cm. Find the volume of the solid so obtained. (Use π = 3.14)
If the areas of three adjacent faces of a cuboid are x, y, z square units, respectively, then the volume of the cuboid is:
A cylindrical water tank has a base radius of 7 m and a height of 10 m. Water is filled into the tank at a constant rate. After filling the tank completely, 5% of the water leaks out due to a crack at the bottom. The remaining water is transferred into another cylindrical tank whose base radius is 5 m. Find the height of water in the second tank.
A cube is painted on all faces and then cut into 27 smaller cubes of equal sizes. How many smaller cubes have exactly two faces painted ?
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.
A solid cube of 4 inches has been painted red, green and black on pair of opposite faces. It has been cut into one inch cubes. How many cubes will have only two faces painted?
From a cuboid of dimension 10cm×5cm×2.5cm, small cubes of edge 2.5 cm are cut. How many small cubes are formed from the cuboid?
The total surface area of a hemisphere is 4,158 . If the radius of the hemisphere becomes one-third of itself, then what will be the new curved surface area of the hemisphere? (Use π=22/7 )
If the volume of a cone is 48π and the height is 10 cm . Find the radius of its base in nearest one decimal place.
