Question 1: From a solid right circular cylinder with height and radius of the base is
a right circular cone of the same height and the same base is removed. Find the volume of the remaining solid.
Answer:
Remaining Volume = Volume of Cylinder – Volume of Cone
Question 2: From a solid cylinder whose height is and radius is
a conical cavity of height
and of base radius
is hollowed out” Find the volume and total surface area of the remaining solid.
Answer:
Cylinder: Height
Cone: Height
Remaining Volume = Volume of Cylinder – Volume of Cone
Surface Area calculations:
Question 3: A circus tent is cylindrical to a height of and conical above it. If its diameter is
and its slant height is
calculate the total area of canvas required. Also, find the total cost of the canvas at
if the width if
Answer:
Cylinder: Height
Cone: Slant Height
Total Surface Area of the tent
Cost of the total canvas
Question 4: A circus tent is cylindrical to a height of surmounted by a conical part. If total height of the tent is
and the diameter of its base is
; calculate: (i) total surface area of the tent, (ii) area of canvas, required to make this tent allowing
of the canvas used for folds and stitching.
Answer:
Cylinder:
Cone:
(ii) Area of canvas
Question 5: A cylindrical boiler, high, is
in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.
Answer:
Cylinder:
Hemisphere:
Question 6: A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is and diameter of hemisphere is
Calculate the capacity and the internal surface area of vessel.
Answer:
Hemisphere:
Question 7: A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is the total height of the toy is
and the radius of the base of the cone = twice the radius of the base of the cylinder
; find the total surface area of the toy. [Take
)
Answer:
Cylinder:
Cone:
Curved surface area of the cylinder
Curved Surface Area of Cone
Area of the base of the Cylinder
Area of the base of the cone
Therefore the total surface area of the toy
Question 8: A cylindrical container with diameter of base contains sufficient water to submerge a rectangular solid of iron with dimensions
Find the rise in level of the water when the solid is submerged.
Answer:
Cylinder:
Volume of iron solid
Question 9: Spherical marbles of diameter are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is
Find how many marbles have been dropped in it if the water rises by
Answer:
Sphere: Radius
Beaker: Radius
Question 10: The cross-section of a railway tunnel is a rectangle
broad and
high surmounted by a semi-circle as shown in: the figure. The tunnel is
long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of
Answer:
Rectangle: Breadth
Semi-circle: Radius
Length of the tunnel
Cost of plastering
Question 11: The horizontal cross-section of a water tank is in the shape of a rectangle with a semi-circle at one end, as shown in the following figure. The water is deep in the tank. Calculate the volume of the water in the tank in gallons.
Answer:
Rectangle: Width
Semi-circle: Radius
Depth of the water
Therefore, water in the tank
Question 12: The given figure shows the cross-section of a water channel consisting of a rectangle and a semi-circle. Assuming that the channel is always full, find the volume of water discharged through it in one minute if water is flowing at the rate of
Give your answer in cubic meters correct to one place of decimal.
Answer:
Rectangle: Length
Semi-circle: Radius
Question 13: An open cylindrical vessel of internal diameter and height
stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is
and height
Find the volume of water required to fill the vessel. If this cone is replaced by another cone, whose height is
and the radius of whose base is
find the drop in the water level.
Answer:
Cylinder:
Cone:
Volume of water required
If the cone was replaced by another cone with then let the drop in water level
. Therefore
Question 14: A cylindrical can, whose base is horizontal and of radius contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate: (i) the total surface area of the can in contact with water when the sphere is in it; (ii) the depth of water in the can before the sphere was Put into the can.
Answer:
Cylinder:
Sphere:
Total Surface Area = Curved Surface area of Cylinder + Area of the base
Let the depth of the water
Question 15: A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is
and height of the cylinder is
Answer:
Cylinder:
Sphere:
Let the height of water when cylinder is upside down