R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 17A

A toy is in the form of a cone of radius $3.5 \mathrm{cm}$ mounted on a hemisphere of same radius on its circular face. The total height of the toy is $15.5 \mathrm{cm}$. Find the total surface area of the toy. if total surface area of toy is $x {\mathrm{cm}}^2$, then $x=?$(Use $\mathrm{\pi }=\frac{22}{7}$)

The given figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.

If the volume of the solid is $k {\mathrm{cm}}^3$, then find $k$ ? (Use $\mathrm{\pi }=\frac{22}{7}$)

From a cubical piece of wood of side $21 \mathrm{cm}$, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece.

After finding above quantities, if total surface area of the remaining piece is $k {\mathrm{cm}}^2$, then find $k$ ? (Use $\mathrm{\pi }=\frac{22}{7}$)

A hemisphere of maximum possible diameter is placed over a cuboidal block of side $7 \mathrm{cm}$. Find the surface area of the solid so formed.

If the surface area of the solid is $k {\mathrm{cm}}^2$, then find $k$ ?

A cubical block of side $10 \mathrm{cm}$ is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of $₹5$ per $100 \mathrm{sq} \mathrm{cm}$. $\mathrm{\pi }=3.14$
If the cost of painting the total surface area of the solid so formed, at the rate of $₹5$ per $100 \mathrm{sq} \mathrm{cm}$ is $₹k$, then find $k$.

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 $5 \mathrm{cm}$ and $13 \mathrm{cm}$ respectively. The radii 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 $30 \mathrm{cm}$.

If the surface area of the toy is $k {\mathrm{cm}}^2$, then find $k$ ?(Use $\mathrm{\pi }=\frac{22}{7}$)

The inner diameter of a glass is $7 \mathrm{cm}$ and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is $16 \mathrm{cm}$ and the apparent capacity of the glass is $p {\mathrm{cm}}^3$, the actual capacity of the glass is $k {\mathrm{cm}}^3$, then find $\left(p+k\right)$. (Correct up to two decimal places and Use $\mathrm{\pi }=\frac{22}{7}$)

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is $26 \mathrm{cm}$ while the height of the conical part is $6 \mathrm{cm}$. The diameter of the base of the conical part is $5 \mathrm{cm}$ and that of the cylindrical part is $4 \mathrm{cm}$. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. $[$Take $\mathrm{\pi }=\frac{22}{7}$]

If the area to be painted by white is $k {\mathrm{cm}}^2$, then find $k$ ?