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VashaNatasha [74]
2 years ago
13

Emily wants to know the volume of a beach ball. She deduces that the beach ball has diameter of 12 inches, and then uses the fol

lowing formula to find the volume: (3.14) (12) V = (3.14) (1728) (5425.92) V=7234.56 cubic inches Emily's answer is incorrect. What did she do wrong? She used the formula for a cylinder instead of the formula for a sphere She used the formula for a sphere instead of the formula for a cone. Multiplying (314)(1728) does not equal 5425.92. She used the beach ball's diameter when she should have used the radius​

Mathematics
1 answer:
Over [174]2 years ago
7 0

Answer:

D. She used the beach's ball's diameter when she should have used the radius

Step-by-step explanation:

To find the volume of the beach ball, using the volume of a sphere is the right formula to use, which is ⁴/3πr³.

The formula she used is correct.

Since the diameter of the ball is assumed to be 12 inches, what is needed to find the volume is the radius.

Radius (r) = ½(diameter) = ½(12) = 6 in.

This is where Emily made a mistake.

She used the diameter of the beach ball instead of its radius (r) which is needed in the equation.

She should have gotten,

V = ⁴/3(3.14)(6)² = 904.32 cubic inches

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Find the sum of the first 47 terms of the following series, to the nearest integer.
Leokris [45]

Answer:

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ is 4,888

Step-by-step explanation:

The given series is;

12, 16, 20, ...,

Therefore, the first term of the series is, a = 12

The common difference of series is found as follows;

The difference between subsequent terms, 12 and 16 is  16 - 12 = 4

The difference between subsequent terms, 16, and 20 is  20 - 16 = 4

Therefore, the common difference, d = 4

The series is therefore an arithmetic projection, AP

The sum of the first 'n' terms of an AP, Sₙ, is given as follows;

S_n = \dfrac{n}{2} \cdot \left [2 \cdot a + (n - 1)\cdot d \right ]

(47/2)*(2*12+(47-1)*4)

The sum of the first 47 terms is therefore given as follows;

S_n = \dfrac{47}{2} \cdot \left [2 \times 12 + (47 - 1)\times 4 \right ] = 4,888

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ = 4,888

5 0
2 years ago
Find the volume of the cone. Round your answer to the nearest tenth.
Sergeu [11.5K]

9514 1404 393

Answer:

  115.5 cubic yards

Step-by-step explanation:

The volume is given by the formula ...\

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Here the diameter is 7 yards, so the radius is 3.5 yards. The volume is then ...

  V = (1/3)π(3.5 yd)²(9 yd) = 36.75π yd³ ≈ 115.454 yd³

The volume of the cone is about 115.5 cubic yards.

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Step-by-step explanation:

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ruslelena [56]
Hello There!

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3 years ago
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