sample problems - volumes.doc

7/28/2019 Sample Problems - Volumes.doc

1/11

Area of a Composite Figure

A figure obtained from combining two different figures is called a composite figure and itsarea,A, isfound by adding together the areas of the individual figures.

Example 21

Find the area of the following composite figure.

Solution:

Find the cost of carpeting a room 10 m long and 8 m wide at $5.50 per square metre.
http://www.mathsteacher.com.au/year10/ch14_measurement/04_plane_figures/19area.htm#areahttp://www.mathsteacher.com.au/year10/ch14_measurement/04_plane_figures/19area.htm#areahttp://www.mathsteacher.com.au/year10/ch14_measurement/04_plane_figures/19area.htm#area


2/11

Solution:

So, the cost of carpeting the room is $440.


3/11

Example 23

A pebble path 1 m wide is to be laid around a square swimming pool, as shown. The quote to supplyand lay the pebble mix is $15 per square metre.

Calculate:a. the area of the pathb. the cost of the path

Solution:


4/11

Example 44

The length of a cuboid is 25 cm, its width is 21 cm, and its volume is 3675 cm. Find its height.

Solution:

So, the height of the cuboid is 7 cm.

Example 45

How many 6 cm cubes will fit into a rectangular box whose internal measurements are 60 cm by 54

cm by 42 cm?

Solution:


5/11


6/11

Example 46

A cylindrical tank of diameter 7 m and depth 4 m is full of water. The water is drained into arectangular prism 11 m long, 7 m wide and 3 m high, as shown in the following diagram.

Solution:

For the cylinder:

Let the height of the water in the prism be h m.


7/11

Volume of a Sphere

If four points on the surface of a sphere are joined to the centre of the sphere, then apyramidof

perpendicular heightr

is formed, as shown in the diagram. Consider the solid sphere to be built with alarge number of such solid pyramids that have a very small base which represents a small portion ofthe surface area of a sphere.
http://www.mathsteacher.com.au/year10/ch14_measurement/19_sphere/20sphere.htm#spherehttp://www.mathsteacher.com.au/year10/ch14_measurement/17_pyramid/20pyramid.htm#pyramidhttp://www.mathsteacher.com.au/year10/ch14_measurement/17_pyramid/20pyramid.htm#pyramidhttp://www.mathsteacher.com.au/year10/ch14_measurement/19_sphere/20sphere.htm#csahttp://www.mathsteacher.com.au/year10/ch14_measurement/19_sphere/20sphere.htm#spherehttp://www.mathsteacher.com.au/year10/ch14_measurement/17_pyramid/20pyramid.htm#pyramidhttp://www.mathsteacher.com.au/year10/ch14_measurement/19_sphere/20sphere.htm#csa


8/11

Example 43

Find the volume of a sphere of radius 9.6 m, rounding your answer to two decimal places.

Solution:

Surface Areas

A solid is a three-dimensional figure. For example, a house brick is a solid, as it is a three-dimensionalfigure.

Many of the solids we come across in our world are combinations of special types of three-dimensional figures such as prisms, cylinders, pyramids, cones and spheres. Measurement of surfacearea is very important to us if we are concerned with the quantities of materials to be used to cover thesurface area.

The sum of the areas of all external surfaces of a three-dimensional object is called its total surfacearea (TSA).

Total Surface Area of a Cube

Recall:

The total surface area (TSA) of a cube is the sum of the areas of its six faces. That is:
http://www.mathsteacher.com.au/year10/ch14_measurement/04_plane_figures/19area.htm#areahttp://www.mathsteacher.com.au/year10/ch14_measurement/04_plane_figures/19area.htm#areahttp://www.mathsteacher.com.au/year10/ch14_measurement/04_plane_figures/19area.htm#areahttp://www.mathsteacher.com.au/year10/ch14_measurement/04_plane_figures/19area.htm#area


9/11

Example 25

Find the total surface area of a box whose edges are all 3.5 cm long.

Solution:

C


10/11

Example 26

Solution:

The total surface area (TSA) of a cuboid is the sum of the areas of its six faces. That is:

Example 27

Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm.

Solution:
http://www.mathsteacher.com.au/year10/ch14_measurement/13_cube/20surf.htm#tsahttp://www.mathsteacher.com.au/year10/ch14_measurement/13_cube/20surf.htm#tsa


11/11

sample problems - volumes.doc

Documents