Apply concepts of density based on area and volume in modeling situations

What is the maximum length of rod that can be placed inside a box having the shape of a cuboid of length $30 \mathrm{cm}$, breadth $24 \mathrm{cm}$ and height $18 \mathrm{cm}?$

The perimeter of a square and a rectangle is$48$ m each. The differences between the areas of the two is $4$ m^$2$. The measurements of the rectangle (in metres) are

If the side of square is increased by 25%, then the area is increased by -

What will be the volume of a right triangular prism if the area of its base is $36 {\mathrm{cm}}^2$ and height is $5 \mathrm{cm}$?

If a regular hexagon is inscribed in a circle of radius $r,$ then its perimeter$?$

A cone, a hemisphere and a cylinder stand on same base and have same height. The ratio of their volumes is _______.

If the area of a circle is equal to the area of a square with side units, what is the diameter of the circle?

The graph of $7x+3y=4$ and $5x-3y=2$, in the $y$-axis at two points having distance -

A circular park of $20 \mathrm{m}$ diameter has a circular path just inside the boundary of width $1 \mathrm{m}$. What is the area of the path?

The volume of a conical tent is $1232 {\mathrm{m}}^3$ and the area of its base is$154 {\mathrm{m}}^2$. Find the length of the canvas required to build the tent if the canvas is $2 \mathrm{m}$ in width. (Take $\pi =\frac{22}{7}$)

Base of right prism is$6 {\mathrm{cm}}^2$. and its height is$7 \mathrm{cm}$ then volume_____.

There is a square park with sides $20 \mathrm{m}$, and there are $2$ diagonal paths that are $2 \mathrm{m}$ wide. Find the area of the park without the paths.

What is the maximum area of a rectangle, the perimeter of which is $18$ $cm$?

$1$$m^3$ is ______________ ?

From a rectangular metal sheet of sides $25 \mathrm{cm}$ and $20 \mathrm{cm}$, a circular sheet as large as possible is cut off. What is the area of the remaining sheet?

A hall is $15 \mathrm{m}$ long and$12 \mathrm{m}$ broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls, the volume of the hall in ${\mathrm{m}}^3$ is _____.

A parallelogram with sides of equal length is called______________.

The area of the triangle is formed by the straight line $3\mathrm{x}+2\mathrm{y}=6$ and the co-ordinate axes is  ______.

What is the area of the circle whose circumference is$264 cm$?

The total area (in sq. unit) of the triangles formed by the graph of $4x+5y=40$, $x$-axis, $y$ -axis and $x=5$ and $y=4$ is ?