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Work out the volume of this prism - OCR - GCSE Maths - Question 6 - 2021 - Paper 1

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Work out the volume of this prism. ![Not to scale](path/to/figure) Dimensions given: - Height: 1 cm - Width: 4 cm - Other Height: 3 cm - Length: 6 cm

Worked Solution & Example Answer:Work out the volume of this prism - OCR - GCSE Maths - Question 6 - 2021 - Paper 1

Step 1

Calculate Volume of the Main Block

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Answer

The volume of the main block can be calculated using the formula for volume of a rectangular prism:

V=extlengthimesextwidthimesextheightV = ext{length} imes ext{width} imes ext{height}

For the main block, the dimensions are:

  • Length = 6 cm
  • Width = 4 cm
  • Height = 1 cm

Thus, the volume is:

V=6imes4imes1=24extcm3V = 6 imes 4 imes 1 = 24 ext{ cm}^3

Step 2

Calculate Volume of the Smaller Block

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Answer

The volume of the smaller block, which has different dimensions, is also calculated using the same formula:

For the smaller block, the dimensions are:

  • Length = 3 cm
  • Width = 4 cm
  • Height = 1 cm

Thus, the volume is:

V=3imes4imes1=12extcm3V = 3 imes 4 imes 1 = 12 ext{ cm}^3

Step 3

Calculate Total Volume

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Answer

To find the total volume of the prism, sum the volumes of both blocks:

extTotalVolume=extVolumeofMainBlock+extVolumeofSmallerBlock ext{Total Volume} = ext{Volume of Main Block} + ext{Volume of Smaller Block}

Substituting the calculated volumes:

extTotalVolume=24+12=36extcm3 ext{Total Volume} = 24 + 12 = 36 ext{ cm}^3

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