Princessdianeaosxf4gidn
Answered

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II. Read and solve each problem.
1. A group of students pitched a tent for their Science camp. The tent's shape is a square pyramid whose base edge is 3 m
and whose height are 2.2 m. How much air is inside the tent?
2. A cylindrical container with a radius of 5 dm and height of 18 dm is filled with gasoline. How much gasoline is in the
container?
3. What is the volume of a cone whose base is radius is 5 cm and whose height is 15 cm?
4. An inflated balloon has a diameter of 30 cm. How much air is inside the balloon?
5. A cylindrical can for storing flour has a radius of 0.3 m and a height of 1.2 m. What is its volume in cubic decimeter?​​

Sagot :

MishSeleniaidn

Direction:

Read and solve each problem.

Answer:

1.) A group of students pitched a tent for their Science camp. The tent's shape is a square pyramid whose base edge is 3 m and whose height are 2.2 m. How much air is inside the tent?

[tex]\mathcal{{Formula:\:V\:=\:s²}}[/tex] [tex]\large{\mathcal{\frac{h}{3}}}[/tex]

  • [tex]\tt{{(\:3\:m\:)²}}[/tex] [tex]\large{\tt{\frac{2.2\:m}{3}}}[/tex]
  • [tex]\tt{{(\:9\:m²\:)\:0.73\:m}}[/tex]
  • [tex]{\boxed{\tt\green{Volume\:=\:6.57\:m³}}}[/tex]

Therefore, the volume of a square pyramid is 6.57 m³.

2.) A cylindrical container with a radius of 5 dm and height of 18 dm is filled with gasoline. How much gasoline is in the container?

[tex]\mathcal{{Formula:\:V\:=\:πr²h}}[/tex]

  • [tex]\tt{{3.14\:(\:5\:dm\:)²(\:18\:dm\:)}}[/tex]
  • [tex]\tt{{3.14\:(\:25\:dm²\:)(\:18\:dm\:)}}[/tex]
  • [tex]\tt{{3.14\:(\:450\:dm²\:)}}[/tex]
  • [tex]{\boxed{\tt\green{Volume\:=\:1,413\:dm³}}}[/tex]

Therefore, the volume of a cylindrical container is 1,413 dm³.

3.) What is the volume of a cone whose base is radius is 5 cm and whose height is 15 cm?

[tex]\mathcal{{Formula:\:V\:=\:πr²}}[/tex] [tex]\large{\mathcal{\frac{h}{3}}}[/tex]

  • [tex]\tt{{(\:3.14\:)(\:5\:cm\:)²}}[/tex][tex]\large{\tt{\frac{15\:cm}{3}}}[/tex]
  • [tex]\tt{{(\:3.14\:)(\:25\:cm²\:)}}[/tex] [tex]\large{\tt{\frac{15\:cm}{3}}}[/tex]
  • [tex]\tt{{3.14\:(\:25\:cm²\:)(\:5\:cm\:)}}[/tex]
  • [tex]\tt{{3.14\:(\:125\:cm²\:)}}[/tex]
  • [tex]{\boxed{\tt\green{Volume\:=\:392.5\:cm³}}}[/tex]

Therefore, the volume of a cone is 392.5 cm³.

4.) An inflated balloon has a diameter of 30 cm. How much air is inside the balloon?

[tex]\mathcal{{Formula:\:V\:=\:}}[/tex] [tex]\large{\mathcal{\frac{1}{6}}}[/tex][tex]\mathcal{{πd³}}[/tex]

  • [tex]\large{\tt{\frac{1}{6}}}[/tex][tex]\tt{{(\:3.14\:)(\:30\:cm\:)³}}[/tex]
  • [tex]\large{\tt{\frac{1}{6}}}[/tex][tex]\tt{{(\:3.14\:)(\:27,000\:cm³\:)}}[/tex]
  • [tex]\large{\tt{\frac{1}{6}}}[/tex][tex]\tt{{(\:84,780\:cm³\:)}}[/tex]
  • [tex]{\boxed{\tt\green{Volume\:=\:14,073.48\:cm³}}}[/tex]

Therefore, the volume of a inflated ballon is 14,073.48 cm³.

5.) A cylindrical can for storing flour has a radius of 0.3 m and a height of 1.2 m. What is its volume in cubic decimeter?

[tex]\mathcal{{Formula:\:V\:=\:πr²h}}[/tex]

  • [tex]\tt{{3.14\:(\:0.3\:m\:)²(\:1.2\:m\:)}}[/tex]
  • [tex]\tt{{3.14\:(\:0.09\:m²\:)(\:1.2\:m\:)}}[/tex]
  • [tex]\tt{{3.14\:(\:0.108\:m²\:)}}[/tex]
  • [tex]{\boxed{\tt\green{Volume\:=\:0.339\:dm³}}}[/tex]

Therefore, the volume of a cylindrical can is 0.339 dm³.

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