QuestionFind the volume of a wooden post (dimensions $8 \mathrm{~cm} \times 5 \mathrm{~cm} \times 22 \mathrm{~cm}$ ) after drilling a hole (diameter $4 \mathrm{~cm}$ ). Round to the nearest tenth.

Studdy Solution

STEP 1

Assumptions1. The post is a right rectangular prism with dimensions $8 \mathrm{~cm}$ by $5 \mathrm{~cm}$ by $22 \mathrm{~cm}$ . A cylindrical hole of diameter $4 \mathrm{~cm}$ is drilled through the post3. The hole goes all the way through the post, so the height of the cylinder is the same as the height of the post4. We need to find the volume of the post after the hole has been drilled5. The volume of the post after the hole has been drilled is the volume of the post minus the volume of the hole

STEP 2

First, we need to find the volume of the post before the hole is drilled. The volume of a right rectangular prism is given by the formula $Volume = Length \times Width \times Height$

STEP 3

Now, plug in the given values for the length, width, and height of the post to calculate its volume.
$Volume =8 \mathrm{~cm} \times5 \mathrm{~cm} \times22 \mathrm{~cm}$

STEP 4

Calculate the volume of the post.
$Volume =8 \mathrm{~cm} \times \mathrm{~cm} \times22 \mathrm{~cm} =880 \mathrm{~cm}^3$

STEP 5

Next, we need to find the volume of the cylindrical hole. The volume of a cylinder is given by the formula $Volume = \pi \times (iameter/2)^2 \times Height$

STEP 6

Now, plug in the given values for the diameter and height of the hole to calculate its volume.
$Volume = \pi \times (4 \mathrm{~cm}/2)^2 \times22 \mathrm{~cm}$

STEP 7

Calculate the volume of the hole.
$Volume = \pi \times (2 \mathrm{~cm})^2 \times22 \mathrm{~cm} =88\pi \mathrm{~cm}^3 \approx276.46 \mathrm{~cm}^3$

STEP 8

Now that we have the volumes of the post and the hole, we can find the volume of the post after the hole has been drilled. This is the volume of the post minus the volume of the hole.
$Volume_{post-drilled} = Volume_{post} - Volume_{hole}$

STEP 9

Plug in the values for the volume of the post and the volume of the hole to calculate the volume of the post after the hole has been drilled.
$Volume_{post-drilled} =880 \mathrm{~cm}^3 -276.46 \mathrm{~cm}^3$

STEP 10

Calculate the volume of the post after the hole has been drilled.
$Volume_{post-drilled} =880 \mathrm{~cm}^3 -276.46 \mathrm{~cm}^3 \approx603.54 \mathrm{~cm}^3$ The volume of the post after the hole has been drilled is approximately $603.54 \mathrm{~cm}^3$ .

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QuestionFind the volume of a wooden post (dimensions $8 \mathrm{~cm} \times 5 \mathrm{~cm} \times 22 \mathrm{~cm}$ ) after drilling a hole (diameter $4 \mathrm{~cm}$ ). Round to the nearest tenth.

Studdy Solution

STEP 1

STEP 2

First, we need to find the volume of the post before the hole is drilled. The volume of a right rectangular prism is given by the formula $Volume = Length \times Width \times Height$

STEP 3

Now, plug in the given values for the length, width, and height of the post to calculate its volume.
$Volume =8 \mathrm{~cm} \times5 \mathrm{~cm} \times22 \mathrm{~cm}$

STEP 4

Calculate the volume of the post.
$Volume =8 \mathrm{~cm} \times \mathrm{~cm} \times22 \mathrm{~cm} =880 \mathrm{~cm}^3$

STEP 5

Next, we need to find the volume of the cylindrical hole. The volume of a cylinder is given by the formula $Volume = \pi \times (iameter/2)^2 \times Height$

STEP 6

Now, plug in the given values for the diameter and height of the hole to calculate its volume.
$Volume = \pi \times (4 \mathrm{~cm}/2)^2 \times22 \mathrm{~cm}$

STEP 7

Calculate the volume of the hole.
$Volume = \pi \times (2 \mathrm{~cm})^2 \times22 \mathrm{~cm} =88\pi \mathrm{~cm}^3 \approx276.46 \mathrm{~cm}^3$

STEP 8

Now that we have the volumes of the post and the hole, we can find the volume of the post after the hole has been drilled. This is the volume of the post minus the volume of the hole.
$Volume_{post-drilled} = Volume_{post} - Volume_{hole}$

STEP 9

Plug in the values for the volume of the post and the volume of the hole to calculate the volume of the post after the hole has been drilled.
$Volume_{post-drilled} =880 \mathrm{~cm}^3 -276.46 \mathrm{~cm}^3$

STEP 10

Calculate the volume of the post after the hole has been drilled.
$Volume_{post-drilled} =880 \mathrm{~cm}^3 -276.46 \mathrm{~cm}^3 \approx603.54 \mathrm{~cm}^3$ The volume of the post after the hole has been drilled is approximately $603.54 \mathrm{~cm}^3$ .

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QuestionFind the volume of a wooden post (dimensions 8 cm×5 cm×22 cm8 \mathrm{~cm} \times 5 \mathrm{~cm} \times 22 \mathrm{~cm}8 cm×5 cm×22 cm) after drilling a hole (diameter 4 cm4 \mathrm{~cm}4 cm). Round to the nearest tenth.

Studdy Solution

STEP 1

STEP 2

First, we need to find the volume of the post before the hole is drilled. The volume of a right rectangular prism is given by the formulaVolume=Length×Width×HeightVolume = Length \times Width \times HeightVolume=Length×Width×Height

STEP 3

Now, plug in the given values for the length, width, and height of the post to calculate its volume.Volume=8 cm×5 cm×22 cmVolume =8 \mathrm{~cm} \times5 \mathrm{~cm} \times22 \mathrm{~cm}Volume=8 cm×5 cm×22 cm

STEP 4

Calculate the volume of the post.Volume=8 cm× cm×22 cm=880 cm3Volume =8 \mathrm{~cm} \times \mathrm{~cm} \times22 \mathrm{~cm} =880 \mathrm{~cm}^3Volume=8 cm× cm×22 cm=880 cm3

STEP 5

Next, we need to find the volume of the cylindrical hole. The volume of a cylinder is given by the formulaVolume=π×(iameter/2)2×HeightVolume = \pi \times (iameter/2)^2 \times HeightVolume=π×(iameter/2)2×Height

STEP 6

Now, plug in the given values for the diameter and height of the hole to calculate its volume.Volume=π×(4 cm/2)2×22 cmVolume = \pi \times (4 \mathrm{~cm}/2)^2 \times22 \mathrm{~cm}Volume=π×(4 cm/2)2×22 cm

STEP 7

Calculate the volume of the hole.Volume=π×(2 cm)2×22 cm=88π cm3≈276.46 cm3Volume = \pi \times (2 \mathrm{~cm})^2 \times22 \mathrm{~cm} =88\pi \mathrm{~cm}^3 \approx276.46 \mathrm{~cm}^3Volume=π×(2 cm)2×22 cm=88π cm3≈276.46 cm3

STEP 8

STEP 9

Plug in the values for the volume of the post and the volume of the hole to calculate the volume of the post after the hole has been drilled.Volumepost−drilled=880 cm3−276.46 cm3Volume_{post-drilled} =880 \mathrm{~cm}^3 -276.46 \mathrm{~cm}^3Volumepost−drilled​=880 cm3−276.46 cm3

STEP 10

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QuestionFind the volume of a wooden post (dimensions $8 \mathrm{~cm} \times 5 \mathrm{~cm} \times 22 \mathrm{~cm}$ ) after drilling a hole (diameter $4 \mathrm{~cm}$ ). Round to the nearest tenth.

First, we need to find the volume of the post before the hole is drilled. The volume of a right rectangular prism is given by the formula $Volume = Length \times Width \times Height$

Now, plug in the given values for the length, width, and height of the post to calculate its volume.
$Volume =8 \mathrm{~cm} \times5 \mathrm{~cm} \times22 \mathrm{~cm}$

Calculate the volume of the post.
$Volume =8 \mathrm{~cm} \times \mathrm{~cm} \times22 \mathrm{~cm} =880 \mathrm{~cm}^3$

Next, we need to find the volume of the cylindrical hole. The volume of a cylinder is given by the formula $Volume = \pi \times (iameter/2)^2 \times Height$

Now, plug in the given values for the diameter and height of the hole to calculate its volume.
$Volume = \pi \times (4 \mathrm{~cm}/2)^2 \times22 \mathrm{~cm}$

Calculate the volume of the hole.
$Volume = \pi \times (2 \mathrm{~cm})^2 \times22 \mathrm{~cm} =88\pi \mathrm{~cm}^3 \approx276.46 \mathrm{~cm}^3$

Plug in the values for the volume of the post and the volume of the hole to calculate the volume of the post after the hole has been drilled.
$Volume_{post-drilled} =880 \mathrm{~cm}^3 -276.46 \mathrm{~cm}^3$