When the length of one of the sides is multiplied by a constant the effect is to multiply the original volume by that constant, as for the example in
[link] .
Right pyramids, right cones and spheres
A pyramid is a geometric solid that has a polygon base and the base is joined to a point, called the apex. Two examples of pyramids are shown in the left-most and centre figures in
[link] . The right-most figure has an apex which is joined to a circular base and this type of geometric solid is called a cone. Cones are similar to pyramids except that their bases are circles instead of polygons.
Surface Area of a Pyramid
The surface area of a pyramid is calculated by adding the area of each face together.
If a cone has a height of
and a base of radius
, show that the surface area is
.
The cone has two faces: the base and the walls. The base is a circle of radius
and the walls can be opened out to a sector of a circle.
This curved surface can be cut into many thin triangles with height close to
(
is called the
slant height ). The area of these triangles will add up to
base
height(of a small triangle) which is
can be calculated by using the Theorem of Pythagoras. Therefore:
We accept the following formulae for volume and surface area of a sphere (ball).
A triangular pyramid is placed on top of a triangular prism. The prism has an equilateral triangle of side length 20 cm as a base, and has a height of 42 cm. The pyramid has a height of 12 cm.
Find the total volume of the object.
Find the area of each face of the pyramid.
Find the total surface area of the object.
We use the formula for the volume of a triangular prism:
We use the formula for the volume of a triangular pyramid:
We note that we can simply add the volumes of each of the two shapes. So we obtain:
. This is the answer to part a.
We note that we have four triangles that make up the pyramid. So the area of each face is simply:
This is the answer to part b.
The total area of the pyramid is simply
The surface area of the prism is:
To find the total surface area, we must subtract the area of one face of the pyramid from the area of the prism. We must also subtract the area of one of the triangular faces of the prism. Doing this gives the total surface area as:
This is the answer to part c.
Calculate the volumes and surface areas of the following solids: *Hint for (e): find the perpendicular height using Pythagoras.
Water covers approximately 71% of the Earth's surface. Taking the radius of the Earth to be 6378 km, what is the total area of land (area not covered by water)?
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life