Photo AI

The diagram shows a prism of length 10cm - OCR - GCSE Maths - Question 4 - 2023 - Paper 5

Question icon

Question 4

The-diagram-shows-a-prism-of-length-10cm-OCR-GCSE Maths-Question 4-2023-Paper 5.png

The diagram shows a prism of length 10cm. The cross-section of the prism is a right-angled triangle. The base, b cm, is 2cm longer than the height, h cm. The volume... show full transcript

Worked Solution & Example Answer:The diagram shows a prism of length 10cm - OCR - GCSE Maths - Question 4 - 2023 - Paper 5

Step 1

Describe the student's error

96%

114 rated

Answer

The student's error is in the computation of the volume of the prism. They correctly set up the relationship between the base and height (b = h + 2) but incorrectly substituted values into the volume formula. The actual volume of a prism is given by:

V=Base Area×LengthV = \text{Base Area} \times \text{Length}

Where the base area of the right-angled triangle is given by:

Base Area=12×base×height=12×b×h\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times b \times h

Combining these formulas, we have:

240=12×b×h×10240 = \frac{1}{2} \times b \times h \times 10

Step 2

Find the correct value of b

99%

104 rated

Answer

Given that b = h + 2,

Substituting the base (b) into the volume equation:

240=12×(h+2)×h×10240 = \frac{1}{2} \times (h + 2) \times h \times 10

Simplifying:

240=5(h2+2h)240 = 5(h^2 + 2h)

Dividing by 5:

48=h2+2h48 = h^2 + 2h

Rearranging gives:

h2+2h−48=0h^2 + 2h - 48 = 0

Factoring this quadratic equation yields:

(h+8)(h−6)=0(h + 8)(h - 6) = 0

Thus, h = 6 or h = -8 (we discard the negative value as height can't be negative). Therefore, h = 6 cm.

Now substituting back to find b:

b=h+2=6+2=8extcmb = h + 2 = 6 + 2 = 8 ext{ cm}

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

;