A cube of side 14 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid?

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01-05-2022
Mathematics

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A cube of side 14 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid?

Sagot :

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ᴜᴋɪʏᴏ ᴜᴋɪʏᴏ · Answer 1 · 2022-05-06T02:23:24-04:00

Answer:

Greatest diameter of hemisphere = 14 cm

Surface area of solid = 1330 cm²

Step-by-step explanation:

Side of the cube (a) = 14 cm

If a cube is surmounted (placed right over its top) by a hemisphere, then that means that the greatest diameter of the hemisphere will be equal to the measure of the edge of the cube (a cube has equal sides). Hence, the greatest diameter of the hemisphere is 14 cm & the radius (r) will be 14/2 = 7 cm (radius = ½ diameter)

Now, we need to find the surface area of the solid.

Here, the solid comprises of a cube & a hemisphere sharing a same circular base area. Hence,

Surface area of the solid

= Surface area of cube + Curved surface of hemisphere - Circular base area

= 6a² + 2πr² - πr²

= 6a² + πr²

= 6(14)² + 22/7×(7)² [π = 22/7]

= 1176 + 154

= 1330 cm²

[tex]\rule{150pt}{2pt}[/tex]

NOTE:

Refer to the attached picture to see how a hemisphere is surmounted on top of a cube.

[tex]\rule{150pt}{2pt}[/tex]

Sagot :

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