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 original pyramid.
Correct answer:
Tips for related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Tip: Our volume units converter will help you convert volume units.
See also our trigonometric triangle calculator.
Tip: Our volume units converter will help you convert volume units.
See also our trigonometric triangle calculator.
You need to know the following knowledge to solve this word math problem:
- geometry
- similarity of triangles
- algebra
- expression of a variable from the formula
- arithmetic
- cube root
- third power
- solid geometry
- similarity bodies
- pyramid
- planimetrics
- area of a shape
- triangle
- square
- basic functions
- percentages
Units of physical quantities:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem: video1
Related math problems and questions:
- Januka
Januka and her father were going to the tent. They found that their old tent was torn. Their mother suggested that they sew a tent whose walls would be made of 4 identical isosceles triangles. Their lower side is 2 m long, and the height is also 2 m. Then - Storage shed
Frank designed a net for a storage shed that he is going to construct out of metal. The design consists of a square base and four square sides, plus four triangular parts that make up the roof. A square base of 6 feet and four square sides, plus 4 feet of - A cone 3
A cone has a diameter of x cm and a slant height of y cm. A square pyramid has a base side length of x cm and a slant height of y cm. Which has the greater surface area? Explain. - Circumference of edges
The hexagon pyramid has a circumference of 120 cm, and the length of the side edge is 25 cm. Calculate its volume.
- The perimeter
The perimeter of the base of a regular quadrilateral pyramid is the same as its height. The pyramid has a volume of 288 dm³. Calculate its surface area round the result to the whole dm². - Calculate 73704
A vertical regular 3-sided pyramid is given. The side of the base a = 5cm, and the height is 8 cm. Calculate the volume and area. - Slant height 2
A regular triangular pyramid with a slant height of 9 m has a volume of 50 m³. Find the lateral area of the pyramid. - Triangular 46641
The regular triangular pyramid ABCDV has a base edge length of 8 cm and a height of 7 cm. Calculate the pyramid's surface area and volume. - The roof
The house's roof has the shape of a regular quadrilateral pyramid 5 m high and the edge of the base 7 m. How many tiles with an area of 540 cm² are needed?
- Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base. - Quadrilateral 44471
The regular quadrilateral pyramid has a surface of 260 cm² and a side wall area of 40 cm². Calculate the length of the base edge and the wall height. - The roof
The tower's roof has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long, and the side wall of the animal with the base at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste. - Quadrilateral 41061
A quadrilateral pyramid has a square base 4 cm long, the height of the pyramid 5 cm, and the height of the wall 5.4 cm. Find the surface and volume of a quadrilateral pyramid. - Pyramid of Giza
The Great Pyramid of Giza has the shape of a regular quadrangular pyramid. The base edge is 227 m long, and the pyramid is 140 m high. What is the weight of the stone needed to build this pyramid if the weight of 1 m³ of stone is 2.5 t?
- Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, and height v = 8 cm. - Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees. - Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.