CIE/GCE/AS/Math/P1/20/Mar/12/Q#3
Question
The diagram shows part of the curve with equation y=x 2+1. The shaded region
enclosed by the curve, the y-axis and the line y = 5 is rotated through 360 o about the y-
axis.
Find the volume obtained.
Solution
Expression for the volume of the solid formed when the shaded region under the curve
𝑥 is rotated completely about the y-axis is;
𝑦=𝑏
𝑉 = ∫ 𝜋 𝑥 2 𝑑𝑦
𝑦=𝑎
Therefore, for the given case;
𝑦=𝑏
𝑉 = ∫ 𝜋 𝑥 2 𝑑𝑥
𝑦=𝑎
Question
The diagram shows part of the curve with equation y=x 2+1. The shaded region
enclosed by the curve, the y-axis and the line y = 5 is rotated through 360 o about the y-
axis.
Find the volume obtained.
Solution
Expression for the volume of the solid formed when the shaded region under the curve
𝑥 is rotated completely about the y-axis is;
𝑦=𝑏
𝑉 = ∫ 𝜋 𝑥 2 𝑑𝑦
𝑦=𝑎
Therefore, for the given case;
𝑦=𝑏
𝑉 = ∫ 𝜋 𝑥 2 𝑑𝑥
𝑦=𝑎
