QuestionFind the area of a circle with radius 13 m. Options: A. $4 m^{2}$ B. $8 m^{2}$ C. $6.28 m^{2}$ D. $12.57 m^{2}$
Calculate the volume of a sphere with radius 13 m. Options: A. $14,356.32 m^{3}$ B. $427.74 m^{3}$ C. $141.58 m^{3}$ D. $161,747.92 m^{3}$
What is the radius of a sphere with surface area $616 cm^{2}$ ? Options: A. $7 cm$ B. $14 cm$ C. $21 cm$ D. $28 cm$
Find the slant height of a cone formed by rolling a semi-circle of radius $10 cm$ . Options: A. $5 cm$ B. $10 cm$ C. $15 cm$

Studdy Solution

STEP 1

Assumptions1. The radius of the circle is13 m. The radius of the sphere is also13 m3. The surface area of another sphere is $616 cm^{}$
4. The radius of the semi-circular region of the paper is $10 cm$

STEP 2

The formula to calculate the area of a circle is given by $Area = \pi r^{2}$ where $r$ is the radius of the circle.

STEP 3

Substitute the given radius into the formula to find the area of the circle.
$Area = \pi (13 m)^{2}$

STEP 4

Calculate the area of the circle.
$Area = \pi (169 m^{2}) =530.66 m^{2}$ None of the given options match the calculated area. There seems to be a mistake in the options provided.

STEP 5

The formula to calculate the volume of a sphere is given by $Volume = \frac{4}{3} \pi r^{3}$ where $r$ is the radius of the sphere.

STEP 6

Substitute the given radius into the formula to find the volume of the sphere.
$Volume = \frac{4}{3} \pi (13 m)^{3}$

STEP 7

Calculate the volume of the sphere.
$Volume = \frac{4}{3} \pi (2197 m^{3}) =9202.77 m^{3}$ None of the given options match the calculated volume. There seems to be a mistake in the options provided.

STEP 8

The formula to calculate the radius of a sphere given its surface area is $r = \sqrt{\frac{Area}{4\pi}}$

STEP 9

Substitute the given surface area into the formula to find the radius of the sphere.
$r = \sqrt{\frac{616 cm^{2}}{4\pi}}$

STEP 10

Calculate the radius of the sphere.
$r = \sqrt{\frac{616 cm^{2}}{12.57}} =7 cm$ The correct option is A. $7 cm$ .

STEP 11

The slant height of a right circular cone formed from a semi-circular region of paper is equal to the radius of the semi-circular region.
Therefore, the slant height of the cone is $10 cm$ .
The correct option is B. $10 cm$ .

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Studdy Solution

STEP 1

Assumptions1. The radius of the circle is13 m. The radius of the sphere is also13 m3. The surface area of another sphere is $616 cm^{}$
4. The radius of the semi-circular region of the paper is $10 cm$

STEP 2

The formula to calculate the area of a circle is given by $Area = \pi r^{2}$ where $r$ is the radius of the circle.

STEP 3

Substitute the given radius into the formula to find the area of the circle.
$Area = \pi (13 m)^{2}$

STEP 4

Calculate the area of the circle.
$Area = \pi (169 m^{2}) =530.66 m^{2}$ None of the given options match the calculated area. There seems to be a mistake in the options provided.

STEP 5

The formula to calculate the volume of a sphere is given by $Volume = \frac{4}{3} \pi r^{3}$ where $r$ is the radius of the sphere.

STEP 6

Substitute the given radius into the formula to find the volume of the sphere.
$Volume = \frac{4}{3} \pi (13 m)^{3}$

STEP 7

Calculate the volume of the sphere.
$Volume = \frac{4}{3} \pi (2197 m^{3}) =9202.77 m^{3}$ None of the given options match the calculated volume. There seems to be a mistake in the options provided.

STEP 8

The formula to calculate the radius of a sphere given its surface area is $r = \sqrt{\frac{Area}{4\pi}}$

STEP 9

Substitute the given surface area into the formula to find the radius of the sphere.
$r = \sqrt{\frac{616 cm^{2}}{4\pi}}$

STEP 10

Calculate the radius of the sphere.
$r = \sqrt{\frac{616 cm^{2}}{12.57}} =7 cm$ The correct option is A. $7 cm$ .

STEP 11

The slant height of a right circular cone formed from a semi-circular region of paper is equal to the radius of the semi-circular region.
Therefore, the slant height of the cone is $10 cm$ .
The correct option is B. $10 cm$ .

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Studdy Solution

STEP 1

Assumptions1. The radius of the circle is13 m. The radius of the sphere is also13 m3. The surface area of another sphere is 616cm616 cm^{}616cm4. The radius of the semi-circular region of the paper is 10cm10 cm10cm

STEP 2

The formula to calculate the area of a circle is given byArea=πr2Area = \pi r^{2}Area=πr2where rrr is the radius of the circle.

STEP 3

Substitute the given radius into the formula to find the area of the circle.Area=π(13m)2Area = \pi (13 m)^{2}Area=π(13m)2

STEP 4

Calculate the area of the circle.Area=π(169m2)=530.66m2Area = \pi (169 m^{2}) =530.66 m^{2}Area=π(169m2)=530.66m2None of the given options match the calculated area. There seems to be a mistake in the options provided.

STEP 5

The formula to calculate the volume of a sphere is given byVolume=43πr3Volume = \frac{4}{3} \pi r^{3}Volume=34​πr3where rrr is the radius of the sphere.

STEP 6

Substitute the given radius into the formula to find the volume of the sphere.Volume=43π(13m)3Volume = \frac{4}{3} \pi (13 m)^{3}Volume=34​π(13m)3

STEP 7

Calculate the volume of the sphere.Volume=43π(2197m3)=9202.77m3Volume = \frac{4}{3} \pi (2197 m^{3}) =9202.77 m^{3}Volume=34​π(2197m3)=9202.77m3None of the given options match the calculated volume. There seems to be a mistake in the options provided.

STEP 8

The formula to calculate the radius of a sphere given its surface area isr=Area4πr = \sqrt{\frac{Area}{4\pi}}r=4πArea​​

STEP 9

Substitute the given surface area into the formula to find the radius of the sphere.r=616cm24πr = \sqrt{\frac{616 cm^{2}}{4\pi}}r=4π616cm2​​

STEP 10

Calculate the radius of the sphere.r=616cm212.57=7cmr = \sqrt{\frac{616 cm^{2}}{12.57}} =7 cmr=12.57616cm2​​=7cmThe correct option is A. 7cm7 cm7cm.

STEP 11

The slant height of a right circular cone formed from a semi-circular region of paper is equal to the radius of the semi-circular region.Therefore, the slant height of the cone is 10cm10 cm10cm.The correct option is B. 10cm10 cm10cm.

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Assumptions1. The radius of the circle is13 m. The radius of the sphere is also13 m3. The surface area of another sphere is $616 cm^{}$
4. The radius of the semi-circular region of the paper is $10 cm$

The formula to calculate the area of a circle is given by $Area = \pi r^{2}$ where $r$ is the radius of the circle.

Substitute the given radius into the formula to find the area of the circle.
$Area = \pi (13 m)^{2}$

Calculate the area of the circle.
$Area = \pi (169 m^{2}) =530.66 m^{2}$ None of the given options match the calculated area. There seems to be a mistake in the options provided.

The formula to calculate the volume of a sphere is given by $Volume = \frac{4}{3} \pi r^{3}$ where $r$ is the radius of the sphere.

Substitute the given radius into the formula to find the volume of the sphere.
$Volume = \frac{4}{3} \pi (13 m)^{3}$

Calculate the volume of the sphere.
$Volume = \frac{4}{3} \pi (2197 m^{3}) =9202.77 m^{3}$ None of the given options match the calculated volume. There seems to be a mistake in the options provided.

The formula to calculate the radius of a sphere given its surface area is $r = \sqrt{\frac{Area}{4\pi}}$

Substitute the given surface area into the formula to find the radius of the sphere.
$r = \sqrt{\frac{616 cm^{2}}{4\pi}}$

Calculate the radius of the sphere.
$r = \sqrt{\frac{616 cm^{2}}{12.57}} =7 cm$ The correct option is A. $7 cm$ .

The slant height of a right circular cone formed from a semi-circular region of paper is equal to the radius of the semi-circular region.
Therefore, the slant height of the cone is $10 cm$ .
The correct option is B. $10 cm$ .