Exercise

The radius and slant height of a cone are in the ratio of $4:7$. If its curved suriace area is $792 {\mathrm{cm}}^2$. Then, its radius is

A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and the diameter of the cylinder part are $21\text{cm} \text{and} 40\text{cm}$respectively, and the height of the cone is $15\text{cm}$, then find the total surface area of the toy. Take $\mathrm{\pi }=3.14.$

If a solid circular cylinder of iron whose diameter is $15 \mathrm{cm}$ and height $10 \mathrm{cm}$ is melted and recast into a sphere, then the radius of sphere is

If a solid right circular cone of height $24 \mathrm{cm}$ and base radius $6 \mathrm{cm}$ is melted and recast in the shape of a sphere, then the radius of the sphere is

A solid piece of iron in the form of a cuboid of dimensions $49 \mathrm{cm}\times 33 \mathrm{cm}\times 24 \mathrm{cm}$ is moulded to form a sphere. The radius of the sphere is

If a cone, a hemisphere and a cylinder have equal bases and have same height, then the ratio of their volumes is

The volume of the largest circular cone that can be carved out from a cube of edge $4.2 \mathrm{cm}$ is

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