Answer:
The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Step-by-step explanation:
Given
Rectangle Pyramid
Base Length = 3x + 1
Base Width = x
Height = 12
Volume = 96
Required
Dimension of the base of the pyramid
Given that the volume of the pyramid is ⅓ of the base area * the height.
This is represented mathematical as
Volume = ⅓ * base area * height.
Where
Base area = width * length
Base area = (3x + 1) * x
Base area = 3x² + x.
So,
Volume becomes
Volume = ⅓ * (3x² + x) * 12.
Volume = (3x² + x) * 4
Substitute 96 for volume
96 = (3x² + x) * 4
Divide both sides by 4
96/4 = (3x² + x) * 4/4
24 = 3x² + x
Subtract 24 fr both sides
24 - 24 = 3x² + x - 24
0 = 3x² + x - 24
3x² + x - 24 = 0
Expand
3x² + 9x - 8x - 24 = 0
Factorize
3x(x + 3) - 8(x + 3) = 0
(3x - 8)(x + 3) = 0
3x - 8 = 0 or x + 3 = 0
3x = 8 or x = -3
x = 8/3 or x = -3
Recall that
Length = 3x + 1
Width = x
For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.
Substitute x = 8/3
Length = 3x + 1
Length = 3(8/3) + 1
Length = 8 + 1
Length = 9
Width = x
Width = 8/3
Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Answer:
30
Step-by-step explanation:
Each one has 10 tenths, so 3 ones have 30 tenths.
You can do this by dividing 3 by 1/10.
3/(1/10) = 3/1 * 10/1 = 30/1 = 30
Answer:
Volume of smaller cone =301.44
Step-by-step explanation:
First let angle of cone be
.
then 
= 3/5 (For bigger triangle)
Same cone angle is for smaller one because they are similar.
= 4/5
Now for smaller cone radius be R
3/5 =R/Slant height
Slant height =5/3R
Lateral surface area =
[R = slant height]
Given lateral surface area =60
=
...................................1
................................................2
Put angle beta in equation 1 and find the value of R
R =6 cm
Height =
Thus volume =
=301.44
C. Plumber A and Plumber B will both charge $135 if they each work 2.5 h.
