Telangana Board Solutions for Chapter: Mensuration, Exercise 4: Exercise

A toy is in the form of a cone mounted on a hemisphere of the same diameter. The diameter of the base and the height of the cone are $6$ $\mathrm{cm}$ and $4$ $\mathrm{cm}$ respectively. Determine the surface area of the toy in ${\mathrm{cm}}^2$. [use $\pi =3.14$].

A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of the common base is $8$ $\mathrm{cm}$ and the heights of the cylindrical and conical portions are $10$ $\mathrm{cm}$ and $6$ $\mathrm{cm}$ respectively. Find the total surface area of the solid in $\mathrm{sq}.\mathrm{cm}$. [use $\pi =3.14$]

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the capsule is $14$ $\mathrm{mm}$ and the thickness is $5$ $\mathrm{mm}$. Find its surface area in ${\mathrm{mm}}^2$.

Two cubes each of volume $64$ ${\mathrm{cm}}^3$ are joined end to end together. Find the surface area of the resulting cuboid in ${\mathrm{cm}}^2$.

A storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of the cylinder be $1.4$ $\mathrm{m}$. and its length be $8$ $\mathrm{m}$. If the cost of painting it on the outside at rate of $₹20$ per ${\mathrm{m}}^2$ is $₹k$, then find the value of $k$. (Correct up to two decimal places)

A sphere, a cylinder and a cone have the same radius and same height. Find the ratio of their volumes. 
[Hint: Diameter of the sphere is equal to the heights of the cylinder and the cone.]

A hemisphere is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the side of the cube. Determine the total surface area of the remaining solid.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is $10$ $\mathrm{cm}$ and its radius of the base is of $3.5$ $\mathrm{cm}$, find the total surface area of the article.