RELATIONSHIPS OF THE VOLUMES OF SOLID FIGURES ( M6MEIVa-95)

 


RELATIONSHIPS OF THE VOLUMES OF SOLID FIGURES


 M6MEIVa-95 - determines the relationship of the volume between a rectangular prism and a

pyramid; a cylinder and a cone; and a cylinder and sphere.

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Determining the relationship of volume between a rectangular prism and a pyramid:

  • The volume of a rectangular prism is length x width x height.
  • The volume of a pyramid is (length x width x height)/3.
  • A rectangular pyramid has one-third the volume of a rectangular prism with the same base and height.

Determining the relationship of volume between a cylinder and a cone:

  • The volume of a cylinder is π x radius² x height.
  • The volume of a cone is (π x radius² x height)/3.
  • A cone has one-third the volume of a cylinder with the same base and height.

Determining the relationship of volume between a cylinder and sphere:

  • The volume of a cylinder is π x radius² x height.
  • The volume of a sphere is (4/3) x π x radius³.
  • A sphere has 1.5 times the volume of a cylinder with the same radius and height.

Other important notes:

  • The volume of a three-dimensional shape is the amount of space it takes up.
  • Formulas for finding the volume of shapes are used to determine the relationship between the volumes of different shapes.
  • Understanding the relationship between the volumes of different shapes can be helpful in many real-life situations, such as calculating the amount of water a container can hold or the amount of soil needed for a garden.

COMPREHENSION QUESTIONS: Direction: Write the letter of the correct answer. Write your answers on your notebook:

1) Which of the following statements is true about the relationship between a rectangular prism and a rectangular pyramid?
A) A rectangular pyramid has twice the volume of a rectangular prism with the same base and height.
B) A rectangular pyramid has one-third the volume of a rectangular prism with the same base and height.
C) A rectangular pyramid has the same volume as a rectangular prism with the same base and height.
D) A rectangular pyramid has four times the volume of a rectangular prism with the same base and height.

2) Which of the following statements is true about the relationship between a cylinder and a cone?
A) A cylinder has half the volume of a cone with the same base and height.
B) A cone has half the volume of a cylinder with the same base and height.
C) A cone has one-third the volume of a cylinder with the same base and height.
D) A cylinder has one-third the volume of a cone with the same base and height.

3) Which of the following formulas can be used to find the volume of a sphere?
A) length x width x height
B) (π x radius² x height)/3
C) π x radius² x height
D) (4/3) x π x radius³

4) Which of the following statements is true about the relationship between a sphere and a cylinder?
A) A sphere has the same volume as a cylinder with the same radius and height.
B) A sphere has twice the volume of a cylinder with the same radius and height.
C) A sphere has 1.5 times the volume of a cylinder with the same radius and height.
D) A sphere has one-third the volume of a cylinder with the same radius and height.

5) What is the formula for finding the volume of a pyramid?
A) π x radius² x height
B) (length x width x height)/3
C) (π x radius² x height)/3
D) (4/3) x π x radius³


TRANSLATION


Pagtukoy sa ugnayan ng volume sa pagitan ng isang parihabang prisma at isang pyramid: Ang dami ng isang parihabang prisma ay haba x lapad x taas. Ang volume ng isang pyramid ay (haba x lapad x taas)/3. Ang isang parihabang pyramid ay may isang-katlo ng dami ng isang parihabang prisma na may parehong base at taas. Pagtukoy sa ugnayan ng volume sa pagitan ng isang silindro at isang kono: Ang volume ng isang silindro ay π x radius² x taas. Ang volume ng isang kono ay (π x radius² x taas)/3. Ang isang kono ay may isang-katlo ng dami ng isang silindro na may parehong base at taas. Pagtukoy sa ugnayan ng volume sa pagitan ng isang silindro at sphere: Ang volume ng isang silindro ay π x radius² x taas. Ang volume ng isang globo ay (4/3) x π x radius³. Ang isang globo ay may 1.5 beses na dami ng isang silindro na may parehong radius at taas. Iba pang mahahalagang tala: Ang dami ng isang three-dimensional na hugis ay ang dami ng espasyong kinukuha nito. Ang mga formula para sa paghahanap ng dami ng mga hugis ay ginagamit upang matukoy ang kaugnayan sa pagitan ng mga volume ng iba't ibang mga hugis. Ang pag-unawa sa kaugnayan sa pagitan ng mga volume ng iba't ibang mga hugis ay maaaring makatulong sa maraming sitwasyon sa totoong buhay, tulad ng pagkalkula ng dami ng tubig na maaaring hawakan ng isang lalagyan o ang dami ng lupa na kailangan para sa isang hardin. MGA TANONG SA PAG-UNAWA: Panuto: Isulat ang titik ng tamang sagot. Isulat ang iyong mga sagot sa iyong kuwaderno: 1) Alin sa mga sumusunod na pahayag ang totoo tungkol sa ugnayan ng isang parihabang prisma at isang parihabang pyramid? A) Ang isang parihabang pyramid ay may dalawang beses sa dami ng isang parihabang prism na may parehong base at taas. B) Ang isang parihabang pyramid ay may isang-katlo ng dami ng isang parihabang prisma na may parehong base at taas. C) Ang isang hugis-parihaba na pyramid ay may parehong dami ng isang parihabang prisma na may parehong base at taas. D) Ang isang parihabang pyramid ay may apat na beses na dami ng isang parihabang prisma na may parehong base at taas. 2) Alin sa mga sumusunod na pahayag ang totoo tungkol sa ugnayan ng isang silindro at isang kono? A) Ang isang silindro ay may kalahati ng dami ng isang kono na may parehong base at taas. B) Ang isang kono ay may kalahati ng volume ng isang silindro na may parehong base at taas. C) Ang isang kono ay may isang-katlo ng dami ng isang silindro na may parehong base at taas. D) Ang isang silindro ay may isang-katlo ng dami ng isang kono na may parehong base at taas. 3) Alin sa mga sumusunod na formula ang maaaring gamitin upang mahanap ang volume ng isang globo? A) haba x lapad x taas B) (π x radius² x taas)/3 C) π x radius² x taas D) (4/3) x π x radius³ 4) Alin sa mga sumusunod na pahayag ang totoo tungkol sa ugnayan ng sphere at cylinder? A) Ang isang sphere ay may parehong volume bilang isang silindro na may parehong radius at taas. B) Ang isang globo ay may dalawang beses sa dami ng isang silindro na may parehong radius at taas. C) Ang isang globo ay may 1.5 beses na dami ng isang silindro na may parehong radius at taas. D) Ang isang globo ay may isang-katlo ng volume ng isang silindro na may parehong radius at taas. 5) Ano ang formula para sa paghahanap ng volume ng isang pyramid? A) π x radius² x taas B) (haba x lapad x taas)/3 C) (π x radius² x taas)/3 D) (4/3) x π x radius³






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