Please help me solve this problems.
1. From a 100cm by 100cm and 60cm block of marble, a pyramid with a square base of 100cm and a height of 60cm was carved. What is the volume of the pyramid? What is the volume of marble removed?
2. If three vertices of a parallelogram are A (2,0), B (4,4), C (6,0), find the fourth vertex D if D is in the 4th quadrant.
3. Two vertices of isosceles triangle ABC are A (0,2) and B (2,2)and AB is the base. Find the vertex C if it is on the x-axis.
Thank you for the help extended.
I will try to help you as well as I can
1. The volume of a pyramide you will find using the following formula found on this page http://www.mathplanet.co...sms,-cylinders-and-cones
where h is the height (in our case 60 cm)
and B is the base area (in our case the area of a square base of 100 cm)
We begin by getting the value of B
The area of a square is the base times the height i.e.
Now we have a value of h and a value of h and can insert them into the formula of the volume of a pyramid
2. Plot the 2 coordinates in a coordinate plane. In a parallelogram two opposite sides are parallel which means that the slope of the line L1 that intersects vertex B and C is the same as the slope of the line L2 that intersects veritces A and D. This means that if we find the slope of the line L1 we can use that to find the coordinates for D
We call the slope m which gives
The slope-intersect form of a linear function as L1 and L2 is
This means that the function of L2 is
To get the value of b we can insert the coordinates for one point on the line (in this case (2, 0) and solve for b
Which gives us the linear function of L2
Then we can do the same but for lines L3 (intesects A and B) and L4 (intersects C and D)
The coordinates of D you will find where L2 and L4 intersect which gives us the following system of equations
Solve for x
To find the corresponding y-value we insert the value of x in either L2 or L4. We use L4
i.e. the coordinates for vertex D is (4, .4)
3.Begin by plotting the points in a coordinate plane.
In an isosceles triangle the two sides that are not tha base are congruent i.e. of the same length.
This means that the distance between A and C is the same as the distance between B and C and we can use this fact together with the distane formula to solve this problem.
The distance formula
We know that the vertex C is on the x-axis which means it has the y-coordinate 0 i.e. the coordinates (x, 0). We also know tha values of A and B which gives us the following equations
Since we know that
we can form the following system of equations
and solve it for x
This means that the coordinates for vertex C is (1, 0)