Math / Geometry

QuestionWhat is the surface area of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\square$ square inches

Studdy Solution

STEP 1

What is this asking? We need to find the total surface area of a cone, meaning the area of the circular base and the curved surface. Watch out! Don't forget to include both parts of the cone's surface area: the circular base and the curved surface.
Also, don't mix up the slant height and the vertical height!

STEP 2

1. Area of the circular base
2. Area of the curved surface
3. Total surface area

STEP 3

The area of a circle is given by the formula $A = \pi \cdot r^2$ , where $r$ is the radius.
We're doing this because the base of the cone is a circle!

STEP 4

We are given that the radius is $r = 11$ inches.
Let's plug that into our formula: $A = \pi \cdot (11)^2$ .

STEP 5

Calculating the area gives us $A = \pi \cdot 121$ .
Remember, $\pi$ is approximately $3.14$ , so $A \approx 3.14 \cdot 121$ .

STEP 6

Multiplying gives us $A \approx 379.94$ square inches.
This is the area of the circular base.
Keep this number in mind, we'll need it later!

STEP 7

The curved surface area of a cone is given by the formula $A = \pi \cdot r \cdot l$ , where $r$ is the radius and $l$ is the slant height.

STEP 8

We know the radius is $r = 11$ inches and the slant height is $l = 17$ inches.
Plugging these values into the formula, we get $A = \pi \cdot 11 \cdot 17$ .

STEP 9

Using our approximation for $\pi$ , we have $A \approx 3.14 \cdot 11 \cdot 17$ .

STEP 10

Multiplying these numbers gives us $A \approx 584.58$ square inches.
This is the area of the curved surface.
Almost there!

STEP 11

To find the total surface area, we add the area of the circular base and the area of the curved surface.

STEP 12

From our previous calculations, the area of the base is approximately $379.94$ square inches, and the area of the curved surface is approximately $584.58$ square inches.

STEP 13

Adding these together, we get $379.94 + 584.58 = 964.52$ square inches.
This is our total surface area!

STEP 14

The surface area of the cone is approximately $964.52$ square inches.

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QuestionWhat is the surface area of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\square$ square inches

Studdy Solution

STEP 1

STEP 2

1. Area of the circular base
2. Area of the curved surface
3. Total surface area

STEP 3

The area of a circle is given by the formula $A = \pi \cdot r^2$ , where $r$ is the radius.
We're doing this because the base of the cone is a circle!

STEP 4

We are given that the radius is $r = 11$ inches.
Let's plug that into our formula: $A = \pi \cdot (11)^2$ .

STEP 5

Calculating the area gives us $A = \pi \cdot 121$ .
Remember, $\pi$ is approximately $3.14$ , so $A \approx 3.14 \cdot 121$ .

STEP 6

Multiplying gives us $A \approx 379.94$ square inches.
This is the area of the circular base.
Keep this number in mind, we'll need it later!

STEP 7

The curved surface area of a cone is given by the formula $A = \pi \cdot r \cdot l$ , where $r$ is the radius and $l$ is the slant height.

STEP 8

We know the radius is $r = 11$ inches and the slant height is $l = 17$ inches.
Plugging these values into the formula, we get $A = \pi \cdot 11 \cdot 17$ .

STEP 9

Using our approximation for $\pi$ , we have $A \approx 3.14 \cdot 11 \cdot 17$ .

STEP 10

Multiplying these numbers gives us $A \approx 584.58$ square inches.
This is the area of the curved surface.
Almost there!

STEP 11

To find the total surface area, we add the area of the circular base and the area of the curved surface.

STEP 12

From our previous calculations, the area of the base is approximately $379.94$ square inches, and the area of the curved surface is approximately $584.58$ square inches.

STEP 13

Adding these together, we get $379.94 + 584.58 = 964.52$ square inches.
This is our total surface area!

STEP 14

The surface area of the cone is approximately $964.52$ square inches.

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QuestionWhat is the surface area of this cone? Use π≈3.14\pi \approx 3.14π≈3.14 and round your answer to the nearest hundredth. □\square□ square inches

Studdy Solution

STEP 1

STEP 2

1. Area of the circular base2. Area of the curved surface3. Total surface area

STEP 3

The area of a circle is given by the formula A=π⋅r2A = \pi \cdot r^2A=π⋅r2, where rrr is the **radius**.We're doing this because the base of the cone is a circle!

STEP 4

We are given that the **radius** is r=11r = 11r=11 inches.Let's plug that into our formula: A=π⋅(11)2A = \pi \cdot (11)^2A=π⋅(11)2.

STEP 5

Calculating the **area** gives us A=π⋅121A = \pi \cdot 121A=π⋅121.Remember, π\piπ is approximately 3.143.143.14, so A≈3.14⋅121A \approx 3.14 \cdot 121A≈3.14⋅121.

STEP 6

Multiplying gives us A≈379.94A \approx 379.94A≈379.94 **square inches**.This is the **area of the circular base**.Keep this number in mind, we'll need it later!

STEP 7

The **curved surface area** of a cone is given by the formula A=π⋅r⋅lA = \pi \cdot r \cdot lA=π⋅r⋅l, where rrr is the **radius** and lll is the **slant height**.

STEP 8

We know the **radius** is r=11r = 11r=11 inches and the **slant height** is l=17l = 17l=17 inches.Plugging these values into the formula, we get A=π⋅11⋅17A = \pi \cdot 11 \cdot 17A=π⋅11⋅17.

STEP 9

Using our approximation for π\piπ, we have A≈3.14⋅11⋅17A \approx 3.14 \cdot 11 \cdot 17A≈3.14⋅11⋅17.

STEP 10

Multiplying these numbers gives us A≈584.58A \approx 584.58A≈584.58 **square inches**.This is the **area of the curved surface**.Almost there!

STEP 11

To find the **total surface area**, we add the **area of the circular base** and the **area of the curved surface**.

STEP 12

From our previous calculations, the **area of the base** is approximately 379.94379.94379.94 square inches, and the **area of the curved surface** is approximately 584.58584.58584.58 square inches.

STEP 13

Adding these together, we get 379.94+584.58=964.52379.94 + 584.58 = 964.52379.94+584.58=964.52 **square inches**.This is our **total surface area**!

STEP 14

The surface area of the cone is approximately 964.52964.52964.52 square inches.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhat is the surface area of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\square$ square inches

1. Area of the circular base
2. Area of the curved surface
3. Total surface area

The area of a circle is given by the formula $A = \pi \cdot r^2$ , where $r$ is the radius.
We're doing this because the base of the cone is a circle!

We are given that the radius is $r = 11$ inches.
Let's plug that into our formula: $A = \pi \cdot (11)^2$ .

Calculating the area gives us $A = \pi \cdot 121$ .
Remember, $\pi$ is approximately $3.14$ , so $A \approx 3.14 \cdot 121$ .

Multiplying gives us $A \approx 379.94$ square inches.
This is the area of the circular base.
Keep this number in mind, we'll need it later!

The curved surface area of a cone is given by the formula $A = \pi \cdot r \cdot l$ , where $r$ is the radius and $l$ is the slant height.

We know the radius is $r = 11$ inches and the slant height is $l = 17$ inches.
Plugging these values into the formula, we get $A = \pi \cdot 11 \cdot 17$ .

Using our approximation for $\pi$ , we have $A \approx 3.14 \cdot 11 \cdot 17$ .

Multiplying these numbers gives us $A \approx 584.58$ square inches.
This is the area of the curved surface.
Almost there!

To find the total surface area, we add the area of the circular base and the area of the curved surface.

From our previous calculations, the area of the base is approximately $379.94$ square inches, and the area of the curved surface is approximately $584.58$ square inches.

Adding these together, we get $379.94 + 584.58 = 964.52$ square inches.
This is our total surface area!

The surface area of the cone is approximately $964.52$ square inches.