From a rectangular solid of metal $42\ cm$ by $30\ cm$ by $20\ cm$, a conical cavity of diameter $14\ cm$ and depth $24\ cm$ is drilled out. Find: the weight of the material drilled out if it weighs $7\ gm$ $per\ cm^3$.
View full solution →Question types
Cylinder, Cone and Sphere question types
261 questions across 5 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
261
Questions
5
Question groups
5
Question types
01
[1 Mark Question Answer]
2 Q→02[2 Mark Question Answer]
52 Q→03[3 marks sum]
99 Q→04[5 marks sum]
49 Q→05[4 marks sum]
59 Q→Sample Questions
Cylinder, Cone and Sphere questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
From a rectangular solid of metal $42 \ cm$ by $30 \ cm$ by $20 \ cm,$ a conical cavity of diameter $14 \ cm$ and depth $24 \ cm$ is drilled out. Find: the weight of the material drilled out if it weighs $7 \ gm$ per $\ cm^3.$
View full solution →Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside thecube.
A solid is in the form of a cone standing one hemi-sphere with both their radii being equal to 8cm and the height of cone is equal to its radius. Find, in terms of $\pi,$ the volume of the solid.
View full solution →A largest sphere is to be carved out of a right circular cylinder of radius $7$ cm and height $14$ cm.Find the volume of the sphere.
View full solution →The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter $10$ cm and the other dimensions are as shown. Calculate: the density of the material if its total weight is $1.7$ kg
View full solution →A solid metallic hemisphere of diameter $28$ cm is melted and recast into a number of identicalsolid cones, each of diameter $14$ cm and height $8$ cm. find the number of cones so formed.
View full solution →In the following diagram a rectangular platform with a semi-circular end on one side is $22$ metreslong from one end to the other end. If the length of the half circumference is $11$ metres. Find thecost of constructing the platform, $1.5$ metres high at the rate of Rs. $4$ per cubic metres.
View full solution →An iron pole consisting of a cylindrical portion $110\ cm$ high and of base diameter $12\ cm$ is surmounted by a cone $9\ cm$ high. Find the mass of the pole, given that $1\ cm^3$ of iron has $8$ gm of mass (approx).
View full solution →The diameter of a sphere is $6\ cm,$ It is melted and drawn into a wire of diameter $0.2\ cm.$ Findthe length of the wire.
View full solution →A conical tent is to accommodate $77$ persons. Each person must have $16m^3$ of air to breathe. Given the radius of the tent as $7m$, find the height of the tent and also its curved surface area.
View full solution →What is the least number of solid metallic spheres, each of $6\ cm$ diameter, that should be meltedand recast to form a solid metal cone whose height is $45\ cm$ and diameter $12\ cm?$
View full solution →A test tube consists of a hemisphere and a cylinder of the same radius. The volume of the water required to fill the whole tube is $\frac{5159}{6} m ^3$ and $\frac{4235}{6} cm ^3$ of water is required to fill the tube toa level which is $4\ cm$ below the top of the tune. Find the radius of the tube and the length of its cylindrical part.
View full solution →A solid, consisting of a right circular cone, standing on 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 the cone is 4 cm. Give your answer to the nearest cubic centimeter.
From a solid cylinder whose height is $16\ cm$ and radius is $12\ cm,$ a conical cavity of height $8\ cm$ and of base radius $6\ cm$ is hollowed out. Find the volume and total surface area of the remaining solid.
View full solution →An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontaltable. Inside this is placed a solid metallic right circular cone, the diameter of whose base is $3 \frac{1}{2}$ cm and height 8 cm. Find the volume of water required to fill the vessel.
If this cone is replaced by another cone, whose height is $1 \frac{3}{4}$ cm and the radius of whose base is2 cm, find the drop in the water level.
View full solution →If this cone is replaced by another cone, whose height is $1 \frac{3}{4}$ cm and the radius of whose base is2 cm, find the drop in the water level.
A buoy is made in the form of hemisphere surmounted by a right cone whose circular basecoincides with the plane surface of hemisphere. The radius of the base of the cone is $3.5$ metres and its volume is two third of the hemisphere. Calculate the height of the cone and the surfacearea of the buoy, correct to two places of decimal
View full solution →The cross-section of a tunnel is a square of side 7m surmounted by a semi circle as shown in theadjoining figure. The tunnel is 80 m long.
(1) its volume
(2) the surface area of the tunnel (excluding the floor) and
(3) its floor area.
(1) its volume
(2) the surface area of the tunnel (excluding the floor) and
(3) its floor area.
A right circular cylinder having diameter $12$ cm and height $15$ cm is full ice-cream. The ice-cream is to be filled in cones of height $12$ cm and diameter $6$ cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
View full solution →An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is $85\ m$ and height of the cylindrical part of $50\ m.$ If the diameter of the base is $168\ m,$ find the quantity of canvas required to make the tent. Allow $20\%$ extra for fold and for stitching. Give your answer to the nearest $m^2.$
View full solution →A cylindrical water tank of diameter $2.8 m$ and height $4.2 m$ is being fed by a pipe of diameter $7 cm$ through which water flows at the rater of $4\ ms^{-1}.$ Calculate, in minutes, the time it takes to fill the tank.
View full solution →A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside.If the height of the cone is $24\ cm,$ the total height of the toy is $60\ cm$ and the radius of the baseof the cone $=$ twice the radius of the base of the cylinder $= 10\ cm;$ find the total surface area ofthe toy.
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