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Dmitrij [34]
3 years ago
14

A hemispherical depression is cut out from one face of a cuboidal wooden block of edge 21cm such that the diameter of the hemisp

here is equal to the edge of the cube. Determine the total surface area of the remaining block
Mathematics
2 answers:
Mandarinka [93]3 years ago
4 0

Answer:

  (2646 +110.25π) cm² ≈ 2992.4 cm²

Step-by-step explanation:

The area of a sphere is 4 times the area of a circle with the same radius. Hence the area of a hemisphere will be 2 times the area of that circle. This means carving a hemispherical depression in the face of the cube will add an area that is equal to the area of the circular hole.

Of course the total surface area of a cube is 6 times the area of one square face. The area of a circle is ...

  A = πr² = π(d/2)² = (π/4)d²

The total surface area of the carved cube is ...

  S = 6·(21 cm)² + (π/4)·(21 cm)² = (441 cm²)(6 +π/4)

  S ≈ 2992.36 cm²

The total surface area of the remaining block is about 2992.4 cm².

joja [24]3 years ago
4 0

Answer:

(2646 +110.25π) cm² ≈ 2992.4 cm²

Step-by-step explanation:

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Answer:

The salespeople earn for the sale of a suit = $13.

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Step-by-step explanation:

Let x be the commission for each suit and y be commission for each pair of shoes.

We have been given that for selling 3 suits and one pair of shoes, Carla has earned $47 in commission. We can represent this information as:

3x+y=47...(1)

We are also told that for selling 7 suits and 2 pairs of shoes, Benicio has earned $107 in commission. We can represent this information as:

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We will use substitution method to solve our system of linear equations. From equation (1) we will get,

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Substituting this value in equation (2) we will get,

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Upon combining like terms we will get,

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