Mathematics, 09.07.2019 04:00 legrandschool1oxa0sd
Find the vector area of a hemispherical bowl of radius r.
Answers: 1
for a surface S
![\text{Now we have }\\ \vec{a} = R^{2}\int_{0}^{\pi /2} sin\theta d\theta \int_{0}^{2\pi}d\phi [sin\theta cos\phi\hat{i}+sin\theta sin\phi \hat{j}+cos\theta \hat{k} ]](/tpl/images/0068/0294/714d9.png)
![=0+0+2{\pi}R^2\hat{k}\int_{0}^{1}(-1)tdt\\ \text {[here} \cos\theta=t\\-sin\theta d\theta=dt]\\= \pi R^2 \hat{k}](/tpl/images/0068/0294/7be8e.png)
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