LUAS PERMUKAAN DAN VOLUME BOLA - BANGUN RUANG SISI LENGKUNG (5) - MATEMATIKA SMP KELAS 9

Summary

In this educational video, Wahyudi S explains the concepts of surface area and volume of a sphere for 9th-grade students. He begins by introducing everyday objects shaped like spheres, such as basketballs and soccer balls, and then defines the sphere as a three-dimensional shape formed by infinitely many circles with equal radii. The video covers the formulas for calculating the surface area (4πr²) and volume (4/3πr³) of a sphere, followed by practical examples and problem-solving. Wahyudi encourages students to actively engage with the content for better understanding.

Takeaways

• 😀 Spheres are common in daily life, with examples like basketballs, tennis balls, volleyballs, ping pong balls, and soccer balls.
• 😀 A sphere is a 3D shape with a curved surface, formed by rotating a circle around its diameter, with all points on the sphere equidistant from the center.
• 😀 The formula for the surface area of a sphere is: 4πr², where r is the radius.
• 😀 The formula for the volume of a sphere is: (4/3)πr³.
• 😀 Surface area and volume calculations rely on the radius, with surface area using the square of the radius and volume using the cube of the radius.
• 😀 If the radius of a sphere is known, both surface area and volume can be calculated directly using the respective formulas.
• 😀 The surface area of a sphere with a radius of 6 cm is 144π cm², and its volume is 288π cm³.
• 😀 Given a sphere's surface area, the radius can be determined by rearranging the surface area formula, allowing the calculation of volume.
• 😀 For a hemisphere (half a sphere), the surface area includes both the curved surface and the base, with separate calculations for each.
• 😀 The surface area of a hemisphere with a radius of 5 cm is 75π cm², including both the curved surface and the circular base.
• 😀 In a problem where the volume of a sphere is given, the radius can be found by rearranging the volume formula, and then the surface area can be calculated.

Q & A

What is the definition of a sphere in geometry?

A sphere is a three-dimensional shape formed by infinitely many circles with the same radius, all centered at the same point, known as the center of the sphere.

What are the formulas for the surface area and volume of a sphere?

The formula for the surface area of a sphere is A = 4πr², and the formula for the volume of a sphere is V = (4/3)πr³.

How can a sphere be formed geometrically?

A sphere can be formed by rotating a semicircle 360° around its diameter. This creates a three-dimensional object with a single curved surface.

What are some real-life objects that resemble a sphere?

Examples of objects that resemble a sphere include a basketball, tennis ball, volleyball, ping-pong ball, and a soccer ball.

How do you calculate the surface area of a sphere with a radius of 6 cm?

To calculate the surface area, use the formula A = 4πr². Substituting r = 6, the surface area is A = 4π(6)² = 144π cm².

How do you calculate the volume of a sphere with a radius of 6 cm?

To calculate the volume, use the formula V = (4/3)πr³. Substituting r = 6, the volume is V = (4/3)π(6)³ = 288π cm³.

If a sphere has a surface area of 144π cm², how do you find the radius?

Use the surface area formula A = 4πr². Given A = 144π, solve for r by dividing both sides by 4π to get r² = 36. Therefore, r = 6 cm.

How do you calculate the volume of a sphere if the radius is 6 cm?

With r = 6 cm, the volume can be calculated using the formula V = (4/3)πr³. Substituting r = 6, the volume is V = (4/3)π(6)³ = 288π cm³.

What is the formula for the surface area of a hemispherical ball?

The surface area of a hemisphere is the sum of the curved surface area and the area of the circular base. The formula is A = 3πr².

How do you find the surface area of a hemisphere with a radius of 5 cm?

For a hemisphere with r = 5 cm, the surface area is A = 3π(5)² = 75π cm².