Tamil Nadu Board Solutions for Chapter: Mensuration, Exercise 16: Exercise 7.3

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter is $14 \mathrm{cm}$ and the height of the vessel is $13 \mathrm{cm}$. If the capacity of the vessel is $V {\mathrm{cm}}^3,$ then find the value of $V$ (rounded off to two decimal places). Assume $\pi =\frac{22}{7}$.

Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is $3 \mathrm{cm}$ and its length is $12 \mathrm{cm}$. If each cone has a height of $2 \mathrm{cm},$ find the volume of the model that Nathan made.

From a solid cylinder whose height is $2.4 \mathrm{cm}$ and the diameter $1.4 \mathrm{cm},$ a cone of the same height and same diameter is carved out. The volume of the remaining solid to the nearest ${\mathrm{cm}}^3$ is $k {\mathrm{cm}}^3$. Find the value of $k$.

A solid consisting of a right circular cone of height $12 \mathrm{cm}$ and radius $6 \mathrm{cm}$ standing on a hemisphere of radius $6 \mathrm{cm}$ is placed upright in a right circular cylinder full of water such that it touches the bottom. The volume of the water displaced out of the cylinder, if the radius of the cylinder is $6 \mathrm{cm}$ and height is $18 \mathrm{cm}$ is $k {\mathrm{cm}}^3$. Find the value of $k$.

A capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. If the length of the entire capsule is $12 \mathrm{mm}$  and the diameter of the capsule is $3 \mathrm{mm},$ $k {\mathrm{mm}}^3$ medicine it can hold. Find the value of $k$.

As shown in figure a cubical block of side $7 \mathrm{cm}$ is surmounted by a hemisphere. If the surface area of the solid is $A {\mathrm{cm}}^2$, then find the value of $A$.

A right circular cylinder just enclose a sphere of radius $r$ units. Calculate the surface area of the sphere, the curved surface area of the cylinder and the ratio of the areas obtained.