Answer: The answer is (a) JD should also subtract the areas of eight hidden surfaces.
Step-by-step explanation: Given that the sculpture consists of five identical prisms and he says the surface area of the sculpture is 4 times the surface area of one prism. We are to choose which one of the given four options are correct.
Since JD is calculating the surface area of the sculpture, consisting of five prisms. So, there will be eight hidden surfaces of the five prisms which will not be in count. Hence, he must subtract the areas of those eight hidden surfaces.
Please see the attached figure for more understanding, where prism A has 1 hidden surface, B has 2 hidden surfaces, C has 2 hidden surfaces, D has 2 hidden surfaces and E has 1 hidden surface.
Thus, the correct option is (a).
Answer:
1) ∫₀¹ 2π x (x − x²) dx
4) ∫₀¹ π ((√y)² − y²) dy
Step-by-step explanation:
The solid formed is a hollow, upside down cone. We can either use washer method or shell method to find the volume.
If we use washer method, the thickness of the washers is dy. The outside radius is R = x₂ = √y, and the inside radius is r = x₁ = y.
Therefore, the volume of each washer is:
dV = π (R² − r²) t
dV = π ((√y)² − y²) dy
The total volume is the sum of all washers from y=0 to y=1.
V = ∫ dV
V = ∫₀¹ π ((√y)² − y²) dy
If we use shell method, the thickness of each shell is dx. The radius of each shell is r = x. The height of each shell is h = y₂ − y₁ = x − x².
Therefore, the volume of each shell is:
dV = 2π r h t
dV = 2π x (x − x²) dx
The total volume is the sum of all shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π x (x − x²) dx
10' x 12' are the dimensions for the floor and roof, both of which will not be covered with wallpaper.
The room will have two identical walls with the following dimensions:
10 x 8
12 x 8
The total area to be covered is:
2 x 10 x 8 + 2 x 12 x 8
Total area = 352 square feet
4/5x + 4/3 = 2x....there are 2 ways to do this...one with fractions, one without.
with :
4/5x + 4/3 = 2x
4/3 = 2x - 4/5x
4/3 = 10/5x - 4/5x
4/3 = 6/5x
4/3 * 5/6 = x
20/18 = x
10/9 = x
without :
4/5x + 4/3 = 2x....multiply by common denominator of 15
12x + 20 = 30x
20 = 30x - 12x
20 = 18x
20/18 = x
10/9 = x