List of top Mathematics Questions on Surface Areas and Volumes

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.

On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream for you.
The slant height of a frustum of a cone is 4 cm and the perimeters (circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
The diagonal of a cube is \(9\sqrt{3}\) cm. Find the total surface area of cube.
If the radius of base of a cone is 7 cm and its height is 24 cm then find its curved surface area.
If the curved surface area of a hemisphere is 1232 cm\(^2\) then its radius is
If the length of the diagonal of a cube is \(2\sqrt{3}\) cm, then the length of its edge is
What is the total surface area of a hemisphere of radius R?
If the edge of a cube is doubled then the total surface area will become how many times of the previous total surface area?
The ratio of the total surface area of a sphere and that of a hemisphere having the same radius is
If the curved surface area of a cone is 880 cm\(^2\) and its radius is 14 cm, then its slant height is
The ratio of the radii of two cylinders is 4 : 5 and the ratio of their heights is 6 : 7, then the ratio of their volumes is
The ratio of the volumes of two spheres is 64 : 125. Then the ratio of their surface areas is

A solid is a cone standing on a hemisphere with both radii $2$ cm and the slant height of the cone $=2\sqrt{2}$ cm. Find the volume of the solid. (Use $\pi=3.14$)

A spherical glass vessel has a cylindrical neck $8$ cm long, $2$ cm in diameter, and the diameter of the spherical part is $8.5$ cm. Find the volume of water that can be filled in it.