Mensuration — CDS Elementary Mathematics PYQs

Let $x$ be the length of a diagonal of a face of a cube and $y$ be the length of a diagonal of the cube. If $x+y=(5+2\sqrt{6})$ units, then what is the total surface area of the cube?

The perimeter of a right-angled isosceles triangle is 20 units. If $\alpha$ is the area of the triangle, then

A sphere of diameter 14 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 14 cm. If the sphere is completely submerged in water, then how much will the level of water rise?

The minute hand of a clock is 15 cm long and sweeps an area of $15\pi$ cm${}^2$ on the dial of the clock. How much angle does it describe during this period?

The diameter of a copper solid sphere is 6 cm. The sphere is melted and recast into a wire. If the diameter of the wire is 0.5 cm, then what is the length of the wire?

A square and a rectangle have the same perimeter $p$ and their areas differ by $q$ units. What is the square of the difference between the length and breadth of the rectangle?

A metallic sheet of rectangular shape is $48$ cm $\times$ $36$ cm. From each corner a square of side $x$ cm is cut off and an open box is made of the remaining sheet. If the box holds 5.12 litre of water, then what is the value of $x$?

The volume of a cube is 8 cm${}^3$ and is equal to the volume of a cuboid of length $x$, breadth $y$ and height $z$, where $x$, $y$ and $z$ are natural numbers $(x>y>z)$. Let $n$ be the number of such cuboids with different dimensions. What is the value of $n$?

Let $x$, $y$, $z$ (all prime) be the length, breadth and height respectively of a cuboid with $x>y>z$. The volume of the cuboid is $30k^3$ cubic units, where $k$ is a natural number. What is the total surface area of the cuboid?

The inside of a bowl is part of a sphere. When water is put into the bowl to a depth $d$, the water surface becomes a circle of radius $2d$. What is the radius of the sphere?