Daisy is making solid spikes for her Halloween costume. The spikes are shaped like right circular cones with base radius of 2 in
1 answer:
She can make 14 spikes maximum
Step-by-step explanation:
The formula of the volume of a cone is V = π r² h, where
- r is the radius of its base
- h is its height
∵ The spikes are shaped like right circular cones with base
radius of 2 inches and height of 6 inches
∴ r = 2 inches
∴ h = 6 inches
- Use the formula above to find the volume of each spike
∵ V = (π)(2)²(6)
∴ V ≅ 25.13274 inches³
∵ Daisy has 360 cubic inches of material for making the spikes
- To find the number of spikes she can make divide the volume
of the material by the volume of each spike
∴ The number of spikes = 360 ÷ 25.13274 = 14.324
- The number of spikes must be an integer
∴ The maximum number of spikes she can make is 14
She can make 14 spikes maximum
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The cost of one roll of plain wrapping paper is $5 and one roll of shiny wrapping paper costs $16.
Step-by-step explanation:
Step 1; Assume that the cost of one roll of plain wrapping paper is $x and a roll of shiny wrapping paper costs $y. so we have the following equations from the given data
4x + 3y = 68, take this as equation 1.
9x + 2y = 77, take this as equation 2
Step 2; We multiply equation 1 with 2 and equation 2 with 3 so we can cancel out the variable y in both equations. By doing this we get
8x + 6y = 136, take this as equation 3,
9x + 2y = 77, this is equation 4.
If we subtract 4 from 3, we cancel out the y variable and can calculate the value of x.
-19x = -103 , x = = 5.
Step 3; Substituting this value of x in any of the previous equations we will get x's value. Here this value of y is substituted in equation 1.
4 (5) + 3y = 68, 20 + 3y = 68 , 3y = 48, y= 16.
So we have x = $5 and y = $16.