Similarity：練習題

Two rectangles are mathematically similar. The smaller rectangle has a width of \(4\text{ cm}\) and a length of \(10\text{ cm}\). The larger rectangle has a width of \(6\text{ cm}\). Calculate the length of the larger rectangle.

Two triangles are mathematically similar. The ratio of their corresponding side lengths is \(2 : 5\). Given that the area of the smaller triangle is \(32\text{ cm}^2\), calculate the area of the larger triangle.

Two solid shapes are mathematically similar. The ratio of their surface areas is \(4 : 9\). Given that the volume of the larger solid is \(540\text{ cm}^3\), calculate the volume of the smaller solid.

Two mathematically similar solid ornaments have volumes of \(125\text{ cm}^3\) and \(216\text{ cm}^3\). The surface area of the smaller ornament is \(100\text{ cm}^2\). Calculate the surface area of the larger ornament.

Two mathematically similar triangles have corresponding sides in the ratio \(2:5\). If the area of the smaller triangle is \(16 \text{ cm}^2\), calculate the area of the larger triangle.

Two mathematically similar containers have heights in the ratio \(2:3\). If the smaller container has a surface area of \(40 \text{ cm}^2\), find the surface area of the larger container.

Two mathematically similar solid pyramids have volumes of \(432 \text{ cm}^3\) and \(2000 \text{ cm}^3\). Given that the surface area of the smaller pyramid is \(108 \text{ cm}^2\), calculate the surface area of the larger pyramid.

Two solid cylinders, A and B, are mathematically similar.
The height of cylinder A is \( 10 \text{ cm} \) and the height of cylinder B is \( 15 \text{ cm} \).

(a) The surface area of cylinder A is \( 80 \text{ cm}^2 \). Calculate the surface area of cylinder B.

(b) The volume of cylinder B is \( 540 \text{ cm}^3 \). Calculate the volume of cylinder A.

Two solid cylinders, A and B, are mathematically similar.
The volume of cylinder A is \(432\pi \text{ cm}^3\) and the volume of cylinder B is \(1024\pi \text{ cm}^3\).

(a) If the height of cylinder A is \(12 \text{ cm}\), calculate the height of cylinder B.

(b) The total surface area of cylinder B is \(640 \text{ cm}^2\). Calculate the total surface area of cylinder A.