PLEASE HELP!
A POINT SOURCE OF LIGHT IS PLACED 50 CM ABOVE A CIRCULAR CARD OF DIAMETER 5CM, THE SOURCE BEING DIRECTLY ABOVE THE CENTRE OF THE CARD. WHAT IS THE AREA OF THE SHADOW ON THE FLOOR 70 CM BELOW THE CARD?
To find the area of the shadow on the floor, we need to consider the geometry of the situation.
Since the point source of light is directly above the center of the circular card, the shadow formed on the floor will also be directly below the card, forming a larger circle.
Here's how you can calculate the area of the shadow on the floor:
1. First, let's find the radius of the larger circle formed on the floor:
Since the diameter of the circular card is 5 cm, the radius would be half of that, which is 5/2 cm or 2.5 cm.
2. Now, let's find the length of the shadow cast on the floor:
The length of the shadow can be determined by similar triangles formed by the height of the card, the length of the shadow, and the distance between the card and the floor.
In this case, the height of the card is 50 cm, and the distance between the card and the floor is 70 cm.
Using the properties of similar triangles, we can set up the following proportion:
height of the card / length of the shadow = distance between the card and the floor / length of the larger shadow on the floor
Plugging in the values, we have:
50 cm / length of the shadow = 70 cm / length of the larger shadow
Rearranging the equation to solve for the length of the larger shadow, we get:
length of the larger shadow = (50 cm * length of the bigger shadow) / 70 cm
Simplifying further, we can cancel out the units and say:
length of the larger shadow = (5/7) * length of the bigger shadow
3. Finally, with the radius of the larger circle and the length of its shadow, we can calculate the area of the shadow on the floor:
The area of a circle can be calculated using the formula: A = π * r^2
So, the area of the shadow on the floor would be:
Area = π * (radius of the larger circle)^2
Area = π * (2.5 cm)^2
Now, we know that the length of the larger shadow is (5/7) * length of the bigger shadow. So the area of the shadow on the floor would be:
Area = π * (2.5 cm)^2 * [(5/7) * length of the bigger shadow]^2
Once you find the length of the bigger shadow cast on the floor, you can substitute it into the equation to find the area.