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A solid ball is made by turning the half circle y =… | StemPy Lab
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A solid ball is made by turning the half circle y = √(36 - x²), for -6 ≤ x ≤ 6, about the x-axis. The lengths are in centimetres. What is the volume of the ball?
Mathematics
Easy
High School (11–12)
Functions and Calculus › Application of Integrals
A-Level
AP
IB
Created by
StemPy Lab
A solid ball is made by turning the half circle
y
=
36
−
x
2
y = \sqrt{36 - x^2}
y
=
36
−
x
2
, for
−
6
≤
x
≤
6
-6 \le x \le 6
−
6
≤
x
≤
6
, about the
x
x
x
-axis. The lengths are in centimetres. What is the volume of the ball?
48
π
cm
3
48\pi\ \text{cm}^3
48
π
cm
3
72
π
cm
3
72\pi\ \text{cm}^3
72
π
cm
3
144
π
cm
3
144\pi\ \text{cm}^3
144
π
cm
3
288
π
cm
3
288\pi\ \text{cm}^3
288
π
cm
3
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← A designer models a cone-shaped lampshade by turning the straight line y = 2x, for 0 ≤ x ≤ 3, about the x-axis. Here x and y are in centimetres. What is the volume of the solid?
The shaded region in the picture lies between the line y = 2x and the parabola y = x². A potter turns it about the x-axis to make a solid with a hollow inside, with x and y in centimetres. What is the volume of the solid? →
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Functions and Calculus › Application of Integrals
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