Mensuration

The sides of a right triangular field are in the ratio $5 : 3 : 4$ and its perimeter is $180$ m. Find the c ost of levelling the field at the rate of Rs. $10$ per square metre.

Rectangle ABCD is inscribed in a circle If AB = 12 cm and BC = 5 cm Find the area of the shaded part (use $\displaystyle \pi =3.14 $)

A triangular copper plate with sides of $3$ cm, $4$ cm and $5$ cm It has three small circular holes cut out of it The radius of each circle is $3$ mm. What is the area of the copper remaining

The geometric figure consists of a right triangle and $2$ semicircles. Find the area of the triangle if the diameter of the two circles are $ 25 \ m $ and $ 12 \ m$ respectively.

Find the area of the shaded design in figure, where $ABCD$ is a square of side $10\ cm$ and semicircles are drawn with each side of the square as diameter. (Use $\pi =3.14$)

Mark the correct alternative of the following. A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ration.

A rectangular metal sheet of area $\displaystyle { 2\ m }^{ 2 }$ is rolled to form a cylinder of volume $\displaystyle { \frac { 4 }{ \pi } \ m^{ 3 } } $. Then the radius of cylinder thus formed is ______ m.

In hcp (ABAB...) and ccp (ABCABC...) structure made up of sphere of equal size ,the volume occupied per sphere (including the empty space ) is (a= radius sphere):

A small sphere of radius $10\ \mathring{A}$ was found to fit perfectly in the largest void of simple cubic arrangement. Find the volume (in $\mathring A ^3$) of the unit cell.

The radius and height of a right circular cone are in the ratio $5:12$ and volume is $2512\,cm$, then find the curved surface area and the total surface area of the cone is