Find the volume and surface area of the composite figure. Give your answer in terms of π.
1 answer:
Answer:
V = 240π cm^3 , S= 168π cm^2
Step-by-step explanation:
The given figure is a combination of hemi-sphere and a cone
<u>Volume:</u>
For volume
r = 6 cm
h = 8 cm
<u>Surface Area:</u>
For this particular figure we have to consider the lateral area of the cone shape and surface area of the hemisphere
We have to find the lateral height
Hence the first option is correct ..
You might be interested in
Step-by-step explanation:
The first step is to find the (b − a) / n factor in the limit of the Riemann sum. This is the Δx.
The next step is to identify the function and the argument, f(xᵢ). The argument xᵢ looks like a + i (b − a) / n.
From there, you can write two equations:
Δx = (b − a) / n
xᵢ = a + i (b − a) / n = a + i Δx
Since you know xᵢ and Δx, you can identify a. And when you know a, you can plug that into Δx to find b. So now you have the limits of the definite integral.
Finally, write the integral using the limits and the function.
Here's an example. Suppose you have the limit:
lim(n→∞) ∑ᵢ₌₁ⁿ √(1 + 3i/n) (3/n)
First, we notice that Δx = (b − a)/n = 3/n. So b − a = 3.
Next, we identify that xᵢ = 1 + 3i/n = a + i (3/n), so a = 1. Therefore, b = 4.
Now, we identify the function, f(xᵢ) = √xᵢ.
Finally, we plug it all into a definite integral:
∫₁⁴ √x dx
