A gift box has the shape of a cube with an edge length of 4.5 in.
What is the volume of the gift box?
Enter your answer in the box.
in3

Answers

Answer 1

Considering the provided information in the given question we have,

A gift box is in the shape of a cube.Length of each edge = 4.5 in

We need to find the volume of the gift box. Since it is in the shape of a cube, we wee need to apply the formula of the volume of a cube. We know that,

→ Volume of cube = l × l × l

→ Volume of cube = 4.5 in × 4.5 in × 4.5 in

→ Volume of cube = [tex] \sf 91.125 \: in^3 [/tex]

Therefore, volume of the gift box is [tex] \bf 91.125 \: in^3 [/tex].


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Answer:

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Answer:

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The greatest common factor( GCF) is = 4.

The greatest common factor(GCF) is the highest number that can divide 8, 44 and 12 without a reminder.

To find the GCF, first list the common factors of each figure given.

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Answers

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Step-by-step explanation:

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Find the area of the composite figure.

Answers

Answer:

B. [tex] 200.5 \: {m}^{2} [/tex]

Step-by-step explanation:

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[tex] = {(12)}^{2} + \frac{1}{2} \pi {r}^{2} \\ \\ = 144 + \frac{1}{2} \times 3.14(6)^{2} \\ \\ = 144 + \frac{1}{2} \times 3.14 \times 36 \\ \\ = 144 + 56.52 \\ \\ = 200.52 \: {m}^{2} \\ \\ \approx \: 200.5 \: {m}^{2} [/tex]

2. Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of . One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping.
(a) One cup has a diameter of 4 in. and a height of 8 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
(b) One cup has a diameter of 8 in. and a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.

Answers

Yes, your answers are correct.

The volume of a cone is given by V = 1/3πr²h.  Since the diameter of the first cone is 4, the radius is 2; therefore the volume is

V = 1/3π(2²)(8) = 32π/3

We divide the volume of the sink, 2000π/3, by the volume of the cone:

2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.

The diameter of the second conical cup is 8, so the radius is 4.  The volume then is:

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Dividing the volume of the sink, 2000π/3, by 128π/3:

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The requried,
(a) Carissa scoop out 63 cups.
(b) Carissa scoop out 16 cups

What is volume?

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The problem requires us to find out how many cups of water Carissa needs to scoop out of the sink to empty it, given the volume of the sink and the dimensions of the two cups. We can solve this problem by using the formula for the volume of a cone:

V = (1/3) * π * r² * h

First, simplify the volume formula for a cone to make it easier to manipulate:

V = 1/3πr²h

Next, plug in the given values for the first cone:

V = 1/3π(2²)(8) = 32π/3

Then, divide the volume of the sink by the volume of the first cone:

2000π/3 ÷ 32π/3 = (2000π/3) * (3/32π) = 2000/32 = 62.5 ≈ 63.

Now, calculate the volume of the second cone using the same formula:

V = 1/3π(4²)(8) = 128π/3

Finally, divide the volume of the sink by the volume of the second cone:

2000π/3 ÷ 128π/3 = (2000π/3) * (3/128π) = 2000/128 = 15.625 ≈ 16.

Divide the volume of the sink by the volume of the first cone to get the number of first cones that can fit into the sink:

2000π/3 ÷ 32π/3 = (2000π/3) * (3/32π) = 2000/32 = 62.5 ≈ 63.

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