surface area (S) of a right rectangular solid is:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
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you have:
L = 7
W = a
H = 4
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formula becomes:
S = 2*7*a + 2*7*4 + 2*a*4
simplify:
S = 14*a + 56 + 8*a
combine like terms:
S = 22*a + 56
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answer is:
S = 22*a + 56 (equation 2)
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to prove, substitute any value for a in equation 2:
let a = 15
S = 22*a + 56 (equation 2)
S = 22*15 + 56
S = 330 + 56
S = 386
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since a = 15, then W = 15 because W = a
go back to equation 1 and substitute 15 for W:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
-----
you have:
L = 7
W = 15
H = 4
-----
equation 1 becomes:
S = 2*7*15 + 2*7*4 + 2*15*4
perform indicated operations:
S = 210 + 56 + 120
S = 386
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surface area is the same using both equations so:
equations are good.
formula for surface area of right rectangle in terms of a is:
S = 22*a + 56
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Question:
The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.
What is the value of h?
Answer:
A. 5
Step-by-step explanation:
Given
Solid Shape: Cone
Volume = 250/7
Diameter = Height
Required
Find the height of the cone
Provided that the diameter (D) and the height (h) are equal; This implies that
D = h ------ (1)
Also, Diameter (D) = 2 * Radius (r)
D = 2r
Substitute 2r for D in (1)
2r = h
Multiply both sides by ½
½ * 2r = ½ * h
r = ½h
Volume of a cone is calculated by;
Volume = ⅓πr²h
⅓πr²h = 250/7
Substitute ½h for r

Take π as 22/7, the expression becomes

Open the bracket

Multiply both sides by 7


Multiply both sides by 3


Multiply both sides by 4



Divide both sides by 22


Take cube root of both sides
![h = \sqrt[3]{136.36}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B136.36%7D)

(Approximated)
Answer:
22.6
Step-by-step explanation:
a^2+b^2=c^2
8^2+b^2=24^2
b^2=512
b=22.6
Answer:
The area of the rectangle A = 25x² - 20x
Step-by-step explanation:
Given
The width of the rectangle = w = 5x - 4
The length of a rectangle = l = 5x
To determine
The area of the rectangle = ?
Using the Formula to determine the area of the rectangle

substitute w = 5x - 4 and l = 5x in the formula

Apply distributive law: a(b-c) = ab - ac


as 5x(5x) = 25x² and 4(5x) = 20x, so

Therefore, the area of the rectangle A = 25x² - 20x
Answer:
Option B, (-9, -5), 3
Step-by-step explanation:
<u>The point slope form in: y - y1 = m(x - x1)</u>
m is the slope
(x1, y1) is the point
<u>Step 1: Determine what the slope and point is their equation</u>
y + 5 = 3(x + 9)
3 is the slope
(-9, -5) is the point
Answer: Option B, (-9, -5), 3