Question
Mathematics Question on Differential Calculus
The volume of the region 𝑅={(𝑥, 𝑦, 𝑧) ∈ ℝ × ℝ × ℝ ∶ 𝑥 2 + 𝑦 2 ≤ 4, 0 ≤ 𝑧 ≤ 4 − 𝑦} is
A
16𝜋-16
B
16𝜋
C
8𝜋
D
16𝜋 + 4
Answer
16𝜋
Explanation
Solution
The correct option is (B): 16𝜋
The volume of the region 𝑅={(𝑥, 𝑦, 𝑧) ∈ ℝ × ℝ × ℝ ∶ 𝑥 2 + 𝑦 2 ≤ 4, 0 ≤ 𝑧 ≤ 4 − 𝑦} is
16𝜋-16
16𝜋
8𝜋
16𝜋 + 4
16𝜋
The correct option is (B): 16𝜋