R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: Exercise 17D

A metallic solid right circular cone is of height $84 \mathrm{cm}$ and the radius of its base is $21 \mathrm{cm}$.  It is melted and recast into a solid sphere. Find the diameter of the sphere.

A toy is in the form of a cone of radius $3.5 \mathrm{cm}$ mounted on a hemisphere of same radius. The total height of the toy is $15.5 \mathrm{cm}$. If the total surface area of the toy is $k {\mathrm{cm}}^2$, then find the value of $k$.

If the radii of the circular ends of a bucket $28 \mathrm{cm}$ high, are $28 \mathrm{cm}$ and $7 \mathrm{cm}$, then find the sum of the numeral values of its capacity and total surface area.

A bucket is in the form of a frustum of a cone with a capacity of $12308.8 {\mathrm{cm}}^3$ of water. The radii of the top and bottom circular ends are $20 \mathrm{cm}$ and $12 \mathrm{cm}$ respectively. Find the height of the bucket. (Use $\mathrm{\pi }=3.14$)

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is $10459\frac{3}{7} {\mathrm{cm}}^3$. The radii of its lower and upper circular ends are $8 \mathrm{cm}$ and $20 \mathrm{cm}$ respectively. Find the cost of metal sheet used in making the container at the rate of $₹1.40 \mathrm{per} {\mathrm{cm}}^2$.

A solid metallic sphere of diameter $28 \mathrm{cm}$ is melted and recast into a number of smaller cones, each of diameter $4\frac{2}{3} \mathrm{cm}$ and height $3 \mathrm{cm}$. Find the number of cones so formed.

A cylindrical vessel with internal diameter $10 \mathrm{cm}$ and height $10.5 \mathrm{cm}$ is full of water. A solid cone of base diameter $7 \mathrm{cm}$ and height $6 \mathrm{cm}$ is completely immersed in water. If the volume of water displaced out of the cylinder is $k {\mathrm{cm}}^3$, then find the value of $k$. ( Use $\pi =\frac{22}{7}$)

A cylindrical vessel with internal diameter $10 \mathrm{cm}$ and height $10.5 \mathrm{cm}$ is full of water. A solid cone of base diameter $7 \mathrm{cm}$ and height $6 \mathrm{cm}$ is completely immersed in water. If the volume of water left in the cylinder is $k {\mathrm{cm}}^3$, then find the value of $k$. (Use $\pi =\frac{22}{7}$)