Photo AI

The diagram shows a cube and a cuboid - Edexcel - GCSE Maths - Question 10 - 2019 - Paper 2

Question icon

Question 10

The-diagram-shows-a-cube-and-a-cuboid-Edexcel-GCSE Maths-Question 10-2019-Paper 2.png

The diagram shows a cube and a cuboid. The total surface area of the cube is equal to the total surface area of the cuboid. Janet says, "The volume of the cube is... show full transcript

Worked Solution & Example Answer:The diagram shows a cube and a cuboid - Edexcel - GCSE Maths - Question 10 - 2019 - Paper 2

Step 1

Find the Surface Area of the Cube

96%

114 rated

Answer

To find the total surface area of the cube, we use the formula:

extSurfaceArea=6s2 ext{Surface Area} = 6s^2

where (s) is the side length of the cube. Given that the side length of the cube is 6 cm:

extSurfaceArea=6×62=6×36=216 cm2 ext{Surface Area} = 6 \times 6^2 = 6 \times 36 = 216 \text{ cm}^2

Step 2

Find the Surface Area of the Cuboid

99%

104 rated

Answer

To find the total surface area of the cuboid, we use the formula:

extSurfaceArea=2(lw+lh+wh) ext{Surface Area} = 2(lw + lh + wh)

where (l), (w), and (h) are the length, width, and height of the cuboid respectively. Given that the dimensions are 8 cm, 6 cm, and 18 cm:

extSurfaceArea=2(8×6+8×18+6×18)=2(48+144+108)=2×300=600 cm2 ext{Surface Area} = 2(8 \times 6 + 8 \times 18 + 6 \times 18) = 2(48 + 144 + 108) = 2 \times 300 = 600 \text{ cm}^2

Step 3

Find the Volume of the Cube

96%

101 rated

Answer

To find the volume of the cube, we use the formula:

extVolume=s3 ext{Volume} = s^3

Thus, for a side length of 6 cm:

extVolume=63=216 cm3 ext{Volume} = 6^3 = 216 \text{ cm}^3

Step 4

Find the Volume of the Cuboid

98%

120 rated

Answer

To find the volume of the cuboid, we use the formula:

extVolume=l×w×h ext{Volume} = l \times w \times h

Using the dimensions of 8 cm, 6 cm, and 18 cm:

extVolume=8×6×18=864 cm3 ext{Volume} = 8 \times 6 \times 18 = 864 \text{ cm}^3

Step 5

Conclusion

97%

117 rated

Answer

Now comparing the volumes, we see:

  • Volume of the cube: 216 cm³
  • Volume of the cuboid: 864 cm³

Since 216 cm³ is not equal to 864 cm³, Janet is incorrect. Thus, the volume of the cube is not equal to the volume of the cuboid.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;