Geometry - JSS3 Mathematics Past Questions and Answers - page 2
Two similar rectangles have lengths in the ratio 2:3. If the area of the smaller rectangle is 36 cm², find the area of the larger rectangle.
Let the scale factor between the rectangles be
𝑘=3/2
Area of the larger rectangle =𝑘^2× Area of the smaller rectangle
Area of the larger rectangle =(3/2)2×36=
Area of the larger rectangle
=9/4×36
Area of the larger rectangle
=81 cm²
Two similar triangles have an area ratio of 9:16. If the smaller triangle has an area of 36 cm², find the area of the larger triangle.
Let the scale factor between the triangles be
𝑘=16/9=4/3
Area of the larger triangle =𝑘^2 × Area of the smaller triangle
Area of the larger triangle =
(4/3)2×36
Area of the larger triangle =16/9×36
Area of the larger triangle
=64 cm²
A cube has a volume of 125 cm³. If a similar cube has a side length twice that of the original cube, find the volume of the larger cube.
Let the scale factor between the cubes be 𝑘=2.
Volume of the larger cube =𝑘 ^3 × Volume of the smaller cube
Volume of the larger cube
=⅔×125
Volume of the larger cube
=8×125
Volume of the larger cube
=1000 cm³
Two similar triangles have sides in the ratio 2:3. If the smaller triangle has a height of 8 cm, find the height of the larger triangle.
Let the scale factor between the triangles be
𝑘=3/2
Height of the larger triangle =𝑘× Height of the smaller triangle
Height of the larger triangle =3/2×8
Height of the larger triangle
=12 cm
A cylinder has a radius of 4 cm and height of 10 cm. If a similar cylinder has a radius of 6 cm, find its height.
Let the scale factor between the cylinders be
𝑘=6/4=3/2 .
Height of the larger cylinder =𝑘× Height of the smaller cylinder
Height of the larger cylinder
=3/2×10
Height of the larger cylinder
=15 cm