pls answer I'll mark brainliest the question is in the picture also show me how you solved the problem.

Mathematics

1 answer:

zzz [600]3 years ago

3 0

Answer:

D 36πa^6b^9

Step-by-step explanation:

Step 1. Write the formula for the volume of a sphere.

V = (4/3)πr³

Step 2. Replace r with the given radius. Since the given radius is an expression, remember to enclose it in parentheses and cube the entire expression.

V = (4/3)π(3a²b³)³

Step 3. Simplify the expression. Start by cubing each factor inside the parentheses.

V = (4/3)π ×(3)³(a²)³(b³)³

To raise an exponent to an exponent, multiply the exponents.

V = (4/3)π × 27a^6b^9

V = (4/3 × 27)πa^6b^9

V = 36πa^6b^9

Answer: D 36πa^6b^9

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1. A circular swimming pool has a diameter of 60 feet, and is surrounded by a concrete sidewalk that is 5 feet wide. What is the

Ivenika [448]

We first calculate the area of the entire pool and the side walk.

Given that the pool has a diameter of 60 feet and that the side walk surrounds the pool with a width of 5 feet. This means that the diameter of the entire pool and the side walk is 60 + 5 + 5 = 70 feet and the radius is 70 / 2 = 35 feet

Thus the area of the entire pool and the side walk is obtained as follows:

$Area=\pi r^2 \\ \\ =\pi(35)^2=1,225\pi\ square\ feet$

Given that the pool has a diameter of 60 feet, this means that the radius of the pool is 30 feet.

Thus the area of the pool is given by:

$Area_{pool}=\pi r^2 \\ \\ =\pi(30)^2=900\pi\ square\ feet$

Therefore, the area of the sidewark is the area of the entire pool and side walk minus the area of the pool, this is given by:

$Area_{side walk}=1,225\pi-900\pi \\ \\ =325\pi=1,021 \ square\ feet.$