Surface Area

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#15000

Surface Area

Cube $$SA=6s^2$$	Rectangular Prism $$SA=2LW+2LH+2WH$$	Triangular Prism $$SA=2(\frac{1}{2}bh)+2sL+bL$$
Pyramid $$SA=LW+the\:sum\:of\: the\: 4\:triangles$$	Cylinder $$SA=2\pi r^2+2\pi rh$$	Open Cylinder $$SA=2\pi r h$$
Open One End Cylinder $$SA=\pi r^2+2\pi r h$$	Cone $$SA= \pi r^2+\pi rL$$	Sphere $$SA=4\pi r^2$$
Truncated Cone $$SA=\pi\, R^2+\pi\,r^2+\pi\,R\,L-\pi\,r\,l$$

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#15004

A sphere has a radius of 10cm. Find:
a. the surface area
b. the volume

a. Surface area = $$4\times\pi\times10^2$$
= 1256.5cm²
Use the surface area formula: $$4\pi r^2$$

b. Volume = $$\frac43\pi\times 10^3$$
= 4188.8cm³Use the volume formula: $$\frac43\pi r^3$$

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#15009

A cylinder, open at one end, has a radius of 10cm and a height of 15cm. Find the surface area.
$$SA=\pi\times10^2+2\times\pi\times10\times20$$
= 1570.80cm²

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#18738

Calculate the surface area of a closed hemisphere with a radius of 5cm. Answer correct to the nearest cm.

Total surface area = half of the sphere plus the circular base

SA = ½ × 4 × π × 5² + π × 5²

SA = 235.619

= 236 cm²

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#18739

A cylinder, open at both ends, has a radius of 10cm and a height of 15cm. Find the surface area.
$$SA=2\times\pi\times10\times20$$ = 1256.64cm2	$$SA=2\pi r h$$ r = 10, h = 20
a. V = 4/3 × π × 2.253 = 47.7cm3	Use the volume formula for a sphere: $$V=\frac{4}{3}\pi r^3$$ and calculate, where r = ½ of the diameter  radius = ½ × 4.5 = 2.25
b. 2 × 1 = 2	If it is 10cm wide, that means it can fit 2 balls across its width.
2 × 1 × 6 = 12 balls	If 5cm high, can only fit one ball.  so if we can fit two per row, and we need 12, so it has to be able to fit six rows along its length, 2 × 1 × 6 = 12 balls
6 × 4.5 = 27cm	now if each ball is 4.5cm in diameter, then 6 balls long to fit the 12, so 6 × 4.5

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#18741

A sphere has a surface area of 200 cm2. Find the radius.
SA = 200 $$200 = 4\pi\;r^2$$	divide both sides by 4$$\pi$$
r2 = 15.915 r = 3.99cm	square root both sides

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