A right triangle with a hypotenuse of 34 cm and a minor cathetus 16 of cm rotates 360° about the major cathetus. What shape does it form? How do you calculate the surface area and volume of the shape it forms?

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A right triangle with a hypotenuse of 34 cm and a minor cathetus 16 of cm rotates 360° about the major cathetus. What shape does it form? How do you calculate the surface area and volume of the shape it forms?

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Answer 1 · 2016-12-03T04:34:18

conical shape. Surface area $S A = 800 π$ $SA= 800pi$ , Volume $V = 2560 π$ $V=2560pi$

Explanation:

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In the diagram above, $l$ $l$ is the hypotenus, $r$ $r$ is the minor cathetus, and $h$ $h$ is the major cathetus.

Surface area $S A = π r^{2} + π r l$ $SA=pir^2+pirl$
Given $l = 34, and r = 16$ $l=34, and r=16$
$\Rightarrow S A = π \cdot 16^{2} + π \cdot 16 \cdot 34 = π \cdot (16^{2} + 16 \cdot 34)$ $=> SA=pi*16^2+pi*16*34=pi*(16^2+16*34)$
$\Rightarrow S A = 800 π = 2513.27$ $=> SA= 800pi=2513.27$

Volume $V = π r^{2} (\frac{h}{3})$ $V=pir^2(h/3)$
$h = \sqrt{l^{2} - r^{2}} = \sqrt{34^{2} - 16^{2}} = 30$ $h=sqrt(l^2-r^2)=sqrt(34^2-16^2)=30$
$\Rightarrow V = π \cdot 16^{2} \cdot (\frac{30}{3}) = 2560 π = 8042.48$ $=> V =pi*16^2*(30/3) = 2560pi =8042.48$

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A right triangle with a hypotenuse of 34 cm and a minor cathetus 16 of cm rotates 360° about the major cathetus. What shape does it form? How do you calculate the surface area and volume of the shape it forms?

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Explanation:

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