Answer:
184.43in².
Step-by-step explanation:
Total surface area of the solid = volume of the cube - the volume of the cone
For the CUBE;
Volume of the cube = L³ where L is the length of one side of the cube.
Since a cone of diameter of 6in is cut into a cube, then the length of the cube will be 6in.
Volume of the cube = 6³ = 216in³
For the CONE;
Volume of the cone = 1/3 πr²h
r is the radius of the cone = diameter/2
r = 6/2 = 3in
slant height l = 4.5in
the height h of the cone will be derived using the Pythagoras theorem.
l² = h²+r²
4.5² = h²+3²
h² = 4.5²-3²
h² = 11.25
h=√11.25
h = 3.35in
Volume of the cone = 1/3 × π × 3²× 3.35
= 31.57in³
Total surface area of the solid = 216in³-31.57in³
= 184.43in²
Answer:

Step-by-step explanation:
The point-slope form of a line:

m - slope
(x₁, y₁) - point
The formula of a slope:

We have the points (-3, 2) and (2, 1). Substitute:


Answer:
1. is a supplementary angle so it adds up to 180 so 180-145=x and x=35
2. is also a supplementary angle so 180-130=x and x =50
Step-by-step explanation:
Answer:
Therefore the dimensions of the garden is 16 feet by 13 feet.
Step-by-step explanation:
Let the length of the garden be x and the width of the garden be y.
Given that the area of the rectangular garden is 208 square feet.
Therefore,
xy =208

Again given that,
The garden is to be surrounded on three sides by a brick wall costing $ 8 per feet and the remaining sides by a fence costing $5 per feet.
The perimeter of the rectangle is = 2(length+ breadth)
= 2(x+y)
=2x+2y
The total cost of fence
![C= [ (2x\times 8)+(y\times 8)+(y\times 5)]](https://tex.z-dn.net/?f=C%3D%20%20%5B%20%282x%5Ctimes%208%29%2B%28y%5Ctimes%208%29%2B%28y%5Ctimes%205%29%5D)
= (16x+ 8y +5y)



To find the maximum or minimum point, we need to find out
and set
=0.

Then





Again 

Therefore at x= 13 , the cost is minimum.
Therefore x = 13 feet.
The other side of the garden is
feet = 16 feet.
Therefore the dimensions of the garden is 16 feet by 13 feet.
Answer: $1090
Step-by-step explanation:
Since Caroline won $205000 in a lottery and then paid $96000 in taxes, the remaining amount will be:
= $205000 - $96000
= $109000
The interest that the account will earn after just 6 months will be:
Interest = PRT
= 109000 × 2% × 6/12
= 109000 × 0.02 × 0.5
= $1090