Step 1 :\(V_{p} = \int_{0}^{\frac{3}{2}\pi} p \sin \left(\frac{1}{3} x\right) \cos \left(\frac{1}{3} x\right) dx\)
Step 2 :\(V_{p} = p \int_{0}^{\frac{3}{2}\pi} \sin \left(\frac{1}{3} x\right) \cos \left(\frac{1}{3} x\right) dx\)
Step 3 :\(V_{p} = p \cdot \frac{3}{2} \left[\frac{1}{2} \sin^{2}\left(\frac{1}{3} x\right)\right]_{0}^{\frac{3}{2}\pi}\)
Step 4 :\(V_{p} = p \cdot \frac{3}{4} \left[\sin^{2}\left(\frac{1}{3}\left(\frac{3}{2}\pi\right)\right) - \sin^{2}\left(\frac{1}{3}(0)\right)\right]\)
Step 5 :\(V_{p} = p \cdot \frac{3}{4} \left[\sin^{2}\left(\frac{1}{2}\pi\right) - \sin^{2}(0)\right]\)
Step 6 :\(V_{p} = p \cdot \frac{3}{4} \left[1 - 0\right]\)
Step 7 :\(V_{p} = \frac{3}{4}p\)
Step 8 :\(\frac{3}{4}p = 10\)
Step 9 :\(p = \frac{40}{3}\)