The triangle PQR above is

Find the value of $\alpha $if the line $2y-\alpha x+4=0$is perpendicular to the line $y+\tfrac{1}{4}x-7=0$

A solid hemisphere has radius 7cm. Find the total surface area (Take $\pi =\tfrac{22}{7} )

A hunter 1.6m tall views a bird on top of a tree at an angle of 45^o. If the distance between the hunter and the tree is 10.4m. Find the height of the tree.

Find the coordinate of the midpoint of x and y intercept of the line $2y=4x-8$

The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?

In the diagram above, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid.

A bucket is 12cm in diameter at the top, 8cm in diameter at the bottom and 4cm deep. Calculate its volume.

In the diagram above are two concentric circles of radii r and R respectively with centre O. If $r=\tfrac{2}{5}R$, express the area of the shaded portion in term of $\pi $and R

If $\tan \theta =\tfrac{4}{3}$, calculate ${{\sin }^{2}}\theta -{{\cos }^{2}}\theta $