List of top Mathematics Questions on Surface Areas and Volumes asked in CBSE Class X

An ice-cream cone of radius $r$ and height $h$ is completely filled by two spherical scoops of ice-cream. If radius of each spherical scoop is $\frac{r}{2}$, then $h : 2r$ equals

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

Three tennis balls are just packed in a cylindrical jar. If radius of each ball is $r$, volume of air inside the jar is

To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are $14 \text{ m} \times 25 \text{ m} \times 16 \text{ m}$.

The internal and external radii of a hollow hemisphere are $5\sqrt{2} \text{ cm}$ and $10 \text{ cm}$ respectively. A cone of height $5\sqrt{7} \text{ cm}$ and radius $5\sqrt{2} \text{ cm}$ is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of $\pi$. (Use $\sqrt{2} = 1.4$)

A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in $ \text{cm}^3 $) is :

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is $ 160 \text{ cm}^2 $.
Reason (R) : The surface area of a cuboid of dimensions $ l \times b \times h $ is $ (lb + bh + hl) $.

The radius of a sphere (in cm) whose volume is $36 \pi \text{ cm}^{3}$, is :

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas are in the ratio $8 : 5$, then find the ratio between the radius of their bases to their height.

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

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 cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are 24 cm × 12 cm × 17 cm.