Similarity bodies - practice problems

Number of problems found: 13

Eiffel Tower
Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material if it weighs is 2.4 kg?
Equilateral cone
We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?
Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current heig
Cone
Circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has an area of 10 cm². Find the area of the or
Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums?
Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
Pizza
Pizza with a diameter 50 cm has a weight 559 g. What diameter will have a pizza weighing 855 g if it is made from the same cloth (same thickness....) and same decorated?
Right circular cone
The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
Two pots
Two similar pots have heights of 16 cm and 10 cm if the smaller pot holds 0,75 l. Find the capacity of the larger pot
Dimensions 4560
The picture frame is made of a 6 cm wide bar. The dimensions of the image are 74 and 57 cm. Are the inner and outer edges of the frame two similar baffles?
Similarity
Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity.
Similarity 30821
There is a given square ABCD with a = 5.3cm. Determine the side size of a similar square if the similarity ratio k = 3cm. Calculate the area and the perimeter of the magnified square

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