Surface Area by Integration Practice Problems Online

The area of the surface obtained by revolving the curve $y = \sqrt{x}$ , $4 \leq x \leq 7$ , about the $x$ -axis can be represented by $\frac{\pi}{6}(a \sqrt{a} - b \sqrt{b})$ . What is the value of $a + b$ ?

The area of the plane $3x+2y+z = 30$ , where $x \geq 0$ , $y \geq 0$ and $z \geq 0$ can be represented by $a \sqrt{b}$ , where $a$ and $b$ are positive integers and $b$ is not divisible by the square of a prime. What is the value of $a+b$ ?

What is the area of the surface obtained by revolving the curve $y=\sqrt{81-x^2}$ from $-2 \leq x \leq 2$ about the $x$ -axis?

Let $S$ be the surface area of the solid obtained by rotating the curve $y = x^3$ $( 0 \leq x \leq 1)$ about the $x$ -axis. If $S = \frac{\pi}{27}(a \sqrt{a} - 1)$ , where $a$ is a positive integer, what is the value of $a$ ?

The area of the paraboloid $z = x^2 + y^2$ , where $0 \leq z \leq 121$ , can be represented by $\frac{\pi}{6} (a \sqrt{a} - 1)$ . What is the value of $a$ ?

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Surface Area by Integration

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