A bookend that weights 0.24 pounds is shaped like a pyramid with square base. How many pounds does a larger similar pyramid-shaped booked weigh if it is made of the same material and each corresponding dimensions is `2(1)/(2)` times as large?

A tent is to be made in the shape of a square pyramid of base edges 6 metres and height 4 metres. How many square metres of canvas needed to make it?

From 5 oranges, 4 mangoes and 2 apples, how many different selection of fruits can be made taking at least one of each kind, if the fruits of the same kind are of different shapes ?

From 5 oranges , 4 mangoes and 2 apples , how many different selections of fruits can be made taking at least one of each kind , if the fruits of the same kind are of different shapes ?

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor. Scale factor= length in image / corresponding length in object. If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200. This means that a length of 1 cm on the photograph above corresponds to a length of 200cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths. What is the actual width of the door if the width of the door in photograph is 0.35cm?

A plot is in the shape of a trapezium. The parallel sides of the plot are 20 m and 16 m long, and the distance between them is 8 m. A square plot has the same area as the trapezium. A pit of dimensions 2.4 m long, 1.5 m wide, and 1 m deep is dug inside the trapezium plot and the soil is spread uniformly on the square plot. Find the rise in the level of hte plot.

Rachel, an engineering student, was asked to make a model shaped like a cyclinder. with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model the Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)