Surface Areas and Volumes — Class 10 Mathematics (Standard) PYQs

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius $10\text{cm}$. Curved surface area of the cavity carved out is (use $\pi =3.14$)

A camping tent in hemispherical shape of radius $1.4\text{m}$, has a door opening of area $0.50{\text{m}}^2$. Outer surface area of the tent is

A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter $7\text{cm}$ is latched with a very thin rod. (Ignore the rod while making calculations.)
Dimensions of the cuboid are $24\text{cm}\times 12\text{cm}\times 17\text{cm}$.
(i) Find the surface area of the bulb.
(ii) What could be the maximum diameter of the bulb if at least $1\text{cm}$ space is left from each side ?
(iii) (a) Find the area of the fabric used if there is a fold of $2\text{cm}$ on top and bottom edges.
OR
(iii) (b) Find the space available inside the lamp.

Assertion (A) : If we join two hemispheres of same radius along their bases, then we get a sphere.
Reason (R): Total Surface Area of a sphere of radius $r$ is $3\pi r^2$.

A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains $\frac{1408}{21}{\text{m}}^3$ of air, find the height of the cylindrical part. (Use $\pi =\frac{22}{7}$).

If the radii of the bases of a cylinder and a cone are in the ratio $3:4$ and their heights are in the ratio $2:3$, find the ratio of their volumes.

Case Study - 3

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is :

The volume of the largest right circular cone that can be carved out from a solid cube of edge $2\text{cm}$ is :

The difference between the outer and inner radii of a hollow right circular cylinder of length $14\text{cm}$ is $1\text{cm}$. If the volume of the metal used in making the cylinder is $176{\text{cm}}^3$, find the outer and inner radii of the cylinder.