The volume provided is 3Pi(x^3) with a radius of x. To determine the volume of a cone, the formula used is V= [1/3]Pi(r^2)*height. By substituting, we get [1/3]Pi(r^2)x = 3Pi(x^3). This simplifies to (r^2)x = 9(x^3). Eventually, we find that r^2 = 9x^2, which leads to r = sqrt[9x^2] = 3x. <span>Answer: r = 3x</span>
Answer:
Volume of the shaded area = (600 - 36π) units³
Step-by-step explanation:
Volume of the shaded area = Volume of pyramid - Volume of cone
Volume of pyramid = ⅓*l*w*h
Where,
l = length of the base of the pyramid = 15 units
w = width of the base of the pyramid = 10 units
h = height of pyramid = 12 units
Substituting the values helps find the volume of the pyramid
Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³
Volume of Cone = ⅓πr²h,
Where,
r = radius = ½ of diameter = ½ of 9 = 3 units
h = height = 12 units
Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12
= π*3*12 = 36π units³
Volume of shaded area = (600 - 36π) units³
$29,580. Breaking it down: 29000/4 equals 7250. So, 7250 plus 2% of 7250 calculates as follows: 7250 + (2/100) * 7250 gives us 7250 + 145, totaling $7395 with four payments resulting in $29,580.
Answer:
The area calculates to 83.905 cm^3
Step-by-step explanation:
The overall ratio is 9 + 7 + 6 = 22
Thus, the side lengths are computed as follows;
9/22 * 44 = 18 cm
7/22 * 44 = 14 cm
6/22 * 44 = 12 cm
Heron’s formula allows us to determine the area of the triangle
First, we calculate s
s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22
Heron’s formula can be expressed as;
A = √s(s-a)(s-b)(s-c)
where a, b, and c are 18, 14, and 12 respectively
Plugging in the values, we obtain;
A = √22(22-18)(22-14)(22-12)
A = √(22 * 4 * 8 * 10)
A = √(7,040)
A = 83.905 cm^3
