Math6 Quarter 4 Week 2 │Problem Solving involving Volume

Summary

This educational video script delves into the concept of volume, explaining it as the measure of space occupied by solid figures. It covers the volume formulas for various shapes, including cubes, rectangular prisms, pyramids, cylinders, cones, and spheres. The script demonstrates how to calculate the volume of each shape with given dimensions, providing step-by-step examples for a rectangular prism, triangular prism, pyramid, cylinder, cone, and sphere. It also includes practical problems, such as calculating the volume of an ice cream cone and a water tank, and concludes with the volume of a cube-shaped chalkbox. The video aims to teach viewers how to solve volume problems in mathematics.

Takeaways

• 📏 Volume is the number of cubic units contained in a space figure.
• 📐 The formula for the volume of a cube is side³ or side × side × side.
• 📦 For a rectangular prism, the volume is length × width × height.
• 🗻 The volume of a square pyramid is (side² × height) / 3.
• 🔺 For a rectangular pyramid, the volume is (length × width × height) / 3.
• 🔵 A cylinder's volume is π × radius² × height.
• 🔺 The volume of a cone is (π × radius² × height) / 3.
• ⚪ The formula for the volume of a sphere is (4/3) × π × radius³.
• 📏 Example: The volume of a rectangular prism with dimensions 7 cm × 3 cm × 4 cm is 84 cubic cm.
• 📐 Example: The volume of a triangular prism with a base of 12 cm, a height of 16 cm, and a prism height of 30 cm is 2880 cubic cm.

Q & A

What is the definition of volume in mathematics?

Volume is the number of cubic units contained in a space figure.

What is the formula for finding the volume of a cube?

The formula for the volume of a cube is \( s^3 \) or side times side times side.

How do you find the volume of a rectangular prism?

The formula for the volume of a rectangular prism is length times width times height.

What is the formula for the volume of a square pyramid?

The formula for the volume of a square pyramid is \( s^2 \times \text{height} / 3 \).

How is the volume of a rectangular pyramid calculated?

The formula for the volume of a rectangular pyramid is length times width times height divided by 3.

What is the formula for finding the volume of a cylinder?

The formula for the volume of a cylinder is \( \pi \times \text{radius}^2 \times \text{height} \).

How do you calculate the volume of a cone?

The formula for the volume of a cone is \( \pi \times \text{radius}^2 \times \text{height} / 3 \).

What is the formula for the volume of a sphere?

The formula for the volume of a sphere is \( 4/3 \times \pi \times \text{radius}^3 \).

How do you find the volume of a rectangular prism with a length of 7 cm, width of 3 cm, and height of 4 cm?

The volume is found by multiplying the length, width, and height: \( 7 \times 3 \times 4 = 84 \) cubic centimeters.

How is the volume of a triangular prism calculated?

The formula for the volume of a triangular prism is base area times height of the prism. For a triangle base, the base area is \( \text{base} \times \text{height} / 2 \).

What is the volume of a triangular prism with a triangle base area of 96 square meters and a height of 30 meters?

The volume is \( 96 \times 30 = 2880 \) cubic meters.

How is the volume of a rectangular pyramid with a length of 6 cm, width of 4 cm, and height of 5 cm calculated?

The volume is \( 6 \times 4 \times 5 / 3 = 40 \) cubic centimeters.

How do you find the volume of a cylinder with a radius of 2.2 cm and a height of 14.6 cm?

The volume is \( \pi \times 2.2^2 \times 14.6 \approx 221.88 \) cubic meters.

What is the volume of a cone with a radius of 6 cm and height of 10 cm?

The volume is \( \pi \times 6^2 \times 10 / 3 \approx 376.8 \) cubic centimeters.

How do you calculate the volume of a sphere with a diameter of 30 cm?

First, find the radius by dividing the diameter by 2, which is 15 cm. Then, use the formula \( 4/3 \times \pi \times 15^3 \approx 14130 \) cubic centimeters.

What is the volume of an ice cream cone with a diameter of 32 mm and height of 45 mm?

The volume is \( \pi \times 16^2 \times 45 / 3 \approx 12057.6 \) cubic millimeters.

How many liters of water can a water tank with an interior height of 10 meters and diameter of 6 meters hold if it is half full?

The tank's volume is \( \pi \times 3^2 \times 10 \approx 282.6 \) cubic meters, so half full it can hold approximately 141.3 cubic meters of water.

What is the volume of a pyramid with a base area of 84 square decimeters and height of 16 decimeters?

The volume is \( 84 \times 16 / 3 = 448 \) cubic decimeters.

How do you find the volume of a chalk box with each edge measuring 18 cm?

The volume is \( 18^3 = 5832 \) cubic centimeters.