Geometry Questions

The base of a parallelogram is twice its height. If the area of the parallelogram is $338{\text{cm}}^2$, then find its height (in $\text{cm}$).

If the radius of a sphere is $2.1\text{cm}$, then find the volume of the sphere.

Tangents $AP$ and $AQ$ are drawn from an external point $A$ to a circle with center $O$. If $\angle APQ=40^{\circ }$, then find $\angle POQ$.

The length of a chord subtended by an arc of a circle is equal to the radius of the circle. If the radius of the circle is $21\text{units}$, then find the length of the arc (in units). (Take $\pi =\frac{22}{7}$)

The chord length of a chord made on an arc of a circle is equal to the radius of the circle. Find the length of the arc (in units), if the radius of the circle is 21 units. (Take $\pi =\frac{22}{7}$)

From an external point $A$, tangents $AP$ and $AQ$ are drawn to a circle with centre $O$. If $\angle APQ=40^{\circ }$, then find $\angle POQ$.

In $\Delta ABC$, $AD$ is the internal bisector of $\angle A$, meeting the side $BC$ at $D$. If $BD=5\text{cm}$ and $BC=7.5\text{cm}$, then the ratio $AB:AC$ is:

The base of a parallelogram is twice its height. If the area of the parallelogram is $338{\text{cm}}^2$, then find its height (in $\text{cm}$).

What is the total surface area of a cone whose radius is $\frac{r}{4}$ and slant height is $4l$?

The volume of a cube is four times the volume of a cuboid. If the sides of the cuboid are $32\text{cm}$, $8\text{cm}$ and $4\text{cm}$, then find the ratio of the total surface area of the cube to that of the cuboid.

Find the area of a minor sector of a circle whose circumference is $88\text{cm}$ and the length of its minor arc is $22\text{cm}$ (use $\pi =\frac{22}{7}$).

What is the length of the arc of a circle whose radius is $35\text{cm}$ and whose arc subtends an angle of $72^{\circ }$ at the centre of the circle?

The volumes of two spheres are in the ratio of $512:3375$. The ratio of their surface areas is:

Two circles with centers $B$ and $D$ have radii $DA=8\text{cm}$ and $BC=x\text{cm}$, respectively. $AC$ is tangent to both circles. If $DB$ and $AC$ intersect at the point $E$, $AE=12\text{cm}$ and $EC=18\text{cm}$, then find the value of $x$ (in $\text{cm}$).

If $L$ is the mid-point of the side $YZ$ of $△XYZ$, and the area of $△XYL$ is $13{\text{cm}}^2$, then the area (in ${\text{cm}}^2$) of $△XYZ$ is:

Find the total surface area of a hemisphere with a radius of $11\text{cm}$?