Answer:
The volume of the cylinder is 108 π units³
Step-by-step explanation:
- The formula of the volume of the cone is V =
πr²h, where r is the radius of its base and h is its height - The formula of the volume of a cylinder is V = πr²h, where r is the radius of its base and h is its height
∵ The area of the base of the cylinder is equal to the area of
the base of the cone
∴ Their radii are equal
∵ The height of the cylinder is equal to the height of the cone
∵ The volume of the cone = 36 π units³
- Equate the formula of the volume of the cone by 36 π
∵ 36 π =
πr²h
- Multiply both sides by 3
∴ 108 π = πr²h
- Divide both sides by π
∴ 108 = r²h
- Substitute the value of r²h in the formula of the volume of
the cylinder
∵ V = πr²h
∴ V = π (108) = 108 π
∴ The volume of the cylinder is 108 π units³
Given:
x = 12 in, y = 16 in and z = 20 in
To find:
The surface area of the geometric shape.
Solution:
Area of top rectangle = z × z
= 20 × 20
Area of top rectangle = 400 in²
Area of middle rectangle = z × y
= 20 × 16
Area of middle rectangle = 320 in²
Area of bottom rectangle = z × x
= 20 × 12
Area of bottom rectangle = 240 in²
Area of left triangle = ![\frac{1}{2}yx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dyx)
![$=\frac{1}{2}\times16\times12](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes16%5Ctimes12)
Area of left triangle = 96 in²
Area of right triangle = ![\frac{1}{2}yx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dyx)
![$=\frac{1}{2}\times16\times12](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes16%5Ctimes12)
Area of right triangle = 96 in²
Surface area = 400 + 320 + 240 + 96 + 96
= 1152
The surface area of the geometric shape is 1152 in².
Answer:
Alright well simplify the expression
Exact form: 16/3 And the decimal form is
Decimal form: 5.3
Mixed number form: 5 1/3 Hope this help's have a nice day :)
Step-by-step explanation:
B. 3
Here’s why
t1 = 3072, r = -1/2
t11 = 3072 (-1/2)^10 = 3