Higher November 2022 Paper 2 Q17
17 The diagram shows two similar solid triangular prisms, A and B.
The volume of prism A is 58.806 cm3
The volume of prism B is 1587.762 cm3
The cross section of each prism is a right-angled triangle.
For prism B:
the length of the base of the triangle is 8.1 cm
the area of the triangle is 43.74 cm2
The height of the triangle for prism A is \(h\) cm.
Work out the value of \(h\). (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 3.6 | P1 | process to find the volume scale factor, eg \(1587.762 \div 58.806\ (= 27)\) or \(58.806 \div 1587.762\ (= 0.037\ldots)\) |
| P1 | process to find the height of B, eg \(2 \times 43.74 \div 8.1\ (= 10.8)\) or process to find the area of A, eg \(43.74 \div (\sqrt[3]{\text{``}27\text{''}})^2\ (= 4.86)\) or \(43.74 \times (\sqrt[3]{\text{``}0.037...\text{''}})^2\ (= 4.86)\) | |
| P1 | complete process to find height of A, eg \(\text{``}10.8\text{''} \div \sqrt[3]{\text{``}27\text{''}}\) or \(\text{``}4.86\text{''} \times 2 \div (8.1 \div \sqrt[3]{\text{``}27\text{''}})\) | |
| A1 | cao |