Mensuration

A right circular cylinder has a base radius of $7\text{ cm}$ and a height of $10\text{ cm}$ as shown in the figure. Calculate the volume of the cylinder. (Take $\pi = \frac{22}{7}$)

If the surface area of a sphere is $616\text{ cm}^2$, find its radius. (Take $\pi = \frac{22}{7}$)

A cone of height $24\text{ cm}$ has a plane base of radius $7\text{ cm}$. Find its curved surface area. (Take $\pi = \frac{22}{7}$)

The volume of a cylinder is $448\pi\text{ cm}^3$ and its height is $7\text{ cm}$. Find its radius.

Find the area of the metal sheet required to make a closed hollow cylinder of height $2.4\text{ m}$ and base diameter $1.4\text{ m}$. (Take $\pi = \frac{22}{7}$)

The ratio of the radii of two cones is $2:3$ and the ratio of their heights is $5:3$. Find the ratio of their volumes.

A lead sphere of radius $12\text{ cm}$ is melted and recast into small bullets of radius $3\text{ cm}$ each. How many bullets can be made?

The sum of the radius of the base and the height of a solid cylinder is $37$ m. If the total surface area of the solid cylinder is $1628$ m$^2$, find the volume of the cylinder. (Take $\pi = \frac{22}{7}$)

A hemispherical tank full of water is emptied by a pipe at the rate of $3\frac{4}{7}$ litres per second. How much time will it take to empty half the tank, if it is $3$ m in diameter? (Take $\pi = \frac{22}{7}$)

A cylindrical container of radius $6$ cm and height $15$ cm is filled with ice-cream. The whole ice-cream is 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 solid piece of iron in the form of a cuboid of dimensions $49$ cm $\times$ $33$ cm $\times$ $24$ cm is melted to form a solid sphere. Find the radius of the sphere.

A solid metallic sphere of radius $6$ cm is melted and recast into small solid cones of radius $2$ cm and height $6$ cm. How many cones are formed?

If a sphere of radius $r$ is melted and cast into the shape of a right circular cylinder of radius $r$, then the height of the cylinder is:

The radius of a sphere is $3$ cm. It is melted and drawn into a wire of radius $0.1$ cm. Find the length of the wire.

The number of coins $1.5$ cm in diameter and $0.2$ cm thick to be melted to form a right circular cylinder of height $10$ cm and diameter $4.5$ cm is:

A vessel is in the form of an inverted cone. Its height is $8$ cm and the radius of its top, which is open, is $5$ cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius $0.5$ cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

A well of diameter $3$ m is dug $14$ m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width $4$ m to form an embankment. Find the height of the embankment.

A farmer connects a pipe of internal diameter $20\text{ cm}$ from a canal into a cylindrical tank in her field, which is $10\text{ m}$ in diameter and $2\text{ m}$ deep. If water flows through the pipe at the rate of $3\text{ km/h}$, in how much time will the tank be filled?

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is $19\text{ cm}$ and the diameter of the cylinder is $7\text{ cm}$. The solid is melted and recast into a solid cube. Find the side of the cube (use $\pi = 22/7$).

A metallic right circular cone of height $20\text{ cm}$ and whose vertical angle is $60^\circ$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}\text{ cm}$, find the length of the wire.

A solid cylinder has a total surface area of $462$ cm$^2$. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder in cm$^3$.

A hemispherical tank full of water is emptied by a pipe at the rate of $3\frac{4}{7}$ litres per second. How much time will it take to empty half the tank, if it is $3$ m in diameter? (Take $\pi = \frac{22}{7}$)

A solid consists of a right circular cone of height $120$ cm and radius $60$ cm standing on a hemisphere of radius $60$ cm. It is placed upright in a right circular cylinder full of water such that it touches the bottom. If the radius of the cylinder is $60$ cm and its height is $180$ cm, find the volume of water left in the cylinder in m$^3$. (Approximate to 2 decimal places)

Three metallic solid spheres of radii $3$ cm, $4$ cm and $5$ cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere in cm.

An iron pillar consists of a cylindrical portion of height $220$ cm and base diameter $24$ cm, which is surmounted by another cylinder of height $60$ cm and radius $8$ cm. Find the mass of the pillar, given that $1$ cm$^3$ of iron has approximately $8$ g mass. (Use $\pi = 3.14$)

A wooden artifact is made by scooping out a hemisphere 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, find the total surface area of the artifact. (Take $\pi = \frac{22}{7}$)

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2$ cm and the diameter of the base is $4$ cm. If a right circular cylinder circumscribes the toy, find the difference between the volumes of the cylinder and the toy. (Take $\pi = 3.14$)

A decorative vessel is made by scooping out a hemisphere from each end of a solid right circular cylinder of height $10$ cm and base radius $3.5$ cm. If the vessel is to be polished on its entire visible surface (inner and outer), calculate the total surface area to be polished. (Use $\pi = \frac{22}{7}$)

A solid toy is in the form of a right circular cylinder with a hemispherical shape on one end and a cone on the other end. Their common radius is $3$ cm and the height of the cylindrical and conical portions are $12$ cm and $4$ cm respectively. Find the total volume of the solid toy. (Take $\pi = 3.14$)

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15$ cm by $10$ cm by $3.5$ cm. The radius of each of the depressions is $0.5$ cm and the depth is $1.4$ cm. Find the volume of wood in the entire stand.