The ratio between the radius of the base and the height of a cylinder is $2 : 3$. If its volume is $1617\ cm^3$, the total surface area of the cylinder is:
- A$308\ cm^2$
- B$462\ cm^2$
- C$540\ cm^2$
- ✓$770\ cm^2$
Answer: D.
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Volume and Surface area of Solids question types
231 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
231
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6
Question groups
5
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M.C.Q (1 Marks)
80 Q→022 Marks Questions
31 Q→033 Marks Question
33 Q→044 Marks Questions
55 Q→051 Marks Question
4 Q→065 Marks Question
28 Q→Sample Questions
Volume and Surface area of Solids questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A metallic cylinder of radius $8 \ cm$ and height $2\ cm$ is melted and converted into a right circular cone of height $6\ cm. $The radius of the base of this cone is:
- A$4\ cm$
- B$5\ cm$
- C$6\ cm$
- ✓$8\ cm$
Answer: D.
View full solution →A mason constructs a wall of dimensions $(270\ cm \times 300\ cm \times 350\ cm)$ with bricks, each of size $(22.5\ cm \times 11.25\ cm \times 8.75\ cm)$ and it is assumed that $1818$ space is covered by the mortar. Number of bricks used to construct the wall is:
- A$11000$
- B$11100$
- ✓$11200$
- D$11300$
Answer: C.
View full solution →The shape of a glass $($tumbler$)$ is usually in the form of:
- AA cylinder.
- ✓Frustum of a cone.
- CA cone.
- DA sphere.
Answer: B.
View full solution →How many bricks, each measuring $(25\ cm \times 11.25\ cm \times 6\ cm),$ will be required to construct a wall $(8m \times 6m \times 22.5\ cm)?$
- A$8000$
- ✓$6400$
- C$4800$
- D$7200$
Answer: B.
View full solution →$66$ cubic cm of silver is drawn into a wire $1mm$ in diameter. Calculate the length of the wire in metres.
View full solution →A solid metallic cuboid of dimension $9m \times 8m \times 2m$ is melted and recast into solid cubes of edge $2\ m.$ Find the number of cubes so formed.
View full solution →The ratio between the radius of the base and the height of a cylinder is $2 : 3$. If the volume of the cylinder is $12936\ cm^3$, then find the radius of the base of the cylinder.
View full solution →A hemispherical bowl of internal radius 9cm is full of water. This water is to be filled in cylindrical bottles of diameter 3cm and height 4cm. Find the number of bottles needed to fill the whole water of the bowl.
The radii of two cylinders are in the ratio of $2 : 3$ and their heights are in the ratio of $5 : 3$. Find the ratio of their volumes.
View full solution →150 spherical marbles, each of diameter 14cm, are dropped in a cylindrical vessel of diameter 7cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.
The volume of a sphere is $4851\ cm^3$. Find its curved surface area.
View full solution →In a corner of a rectangular field with dimensions 35m × 22m, a well with 14m inside diameter is dug 8m deep. The earth dug out is spread evenly over the remaining part of the field. Find the rise in the level of the field.
The surface areas of two spheres are in the ratio of 4 : 25. Find the ratio of their volumes.
A 5-m-wide cloth is used to make a conical tent of base diameter 14m and height 24m. Find th cost of cloth used at the rate of Rs. 25 per metre.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5cm and 13cm respectively. The radi of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30cm.
A cylindrical container of radius 6cm and height 15cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice cream cone.
A cylindrical vessel with internal diameter 10cm and height 10.5cm is full of water. A solid cone of base diameter 7cm and height 6cm is completely immersed in water. Find the volume of water
- Displaced out of the cylinder
- Left in the cylinder.
The height of a right circular cone is 20cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be $\frac{1}{8}$ of the volume of the given cone, then at what height above the base is the section made?
View full solution →A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is $10\ cm$ and its base is of radius $3.5\ cm$, then find the volume of wood in the toy.
View full solution →Find the number of solid spheres, each of diameter 6cm, that could be moulded to form a solid metallic cylinder of height 45cm and diameter 4cm.
The radii of the top and bottom of a bucket of slant height 45cm are 28cm and 7cm, respectively. Find the curved surface area of the bucket.
Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii?
A circus tent is cylindrical to a height of $4\ m$ and conical above it. If its diameter is $105\ m$ and its slant height is $40\ m$, then find the total area of the canvas required.
View full solution →A tent is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20m and 6m, respectively, and the height is 24m. If the height of the tent is 28m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required. $\Big[\text{Take }\pi=\frac{22}{7}.\Big]$
View full solution →A bucket of height 24cm is in the form of frustum of a cone whose circular ends are of diameter 28cm and 42cm. Find the cost of milk at the rate of ₹ 30 per litre, which the bucket can hold.
A right triangle whose sides are 15cm and 20cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of $\pi$ as found appropriate)
View full solution →A medicine capsule is in the shape of a cylinder with two hemipheres stuck to each of its ends. The length of the entire capsule is 14mm and the diameter of the capsule is 5mm. Fin its surface area.
The perimeters of the two circular ends of a frustum of a cone are 48cm and 36cm. If the height of the frustum is 11cm, then find its volume and curved surface area.
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