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Solved problems for the chapter:

Surface Area of 3-Dimensional Shapes

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Geometric sequence

1. General term of a geometric sequence

1.1. Common ratio of a geometric sequence

2. Geometric mean

2.1. Relationship between geometric and arithmetic mean

2.1.1. Numerical Proof

2.1.2. Graphical proof

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:surface_area_of_3-dimensional_shapes/4117/

Example 1.

The radius r of a cone measures and the area of the curved surface measures . Calculate the height of the cone.

Example 2.

Calculate the total surface area and volume of a cuboid with sides , b = 4 cm and c = 5 cm.

Which figure is obtained by cutting with the plane on which the height of the cylinder lies:

upright cylinder
equilateral cylinder?

What do we call the plot thus obtained?

Calculate the area and volume of a school mushroom 20 cm long, 10 cm wide and 5 cm high.

The curved surface area CSA of a cone measures and the slant height measures . Calculate the total surface area TSA of the cone.

Write the labelled part of the pyramid on the lines. Is the pyramid a 2-dimensional or 3-dimensional body?

A pyramid has a triangle of size as its base face, and the lateral surface area of its is . What is the to total surface area of this pyramid?

A pyramid has a rectangular base with a base area of size , and lateral surface consists of two pairs of triangles with areas and . What is the total surface area of this pyramid?

Name the pyramids below

10.

The base area of a square base pyramid with total surface area of measures . What is the area of the each face of the pyramid?

11.

The base area of a triangular base pyramid with volume measures . How high is the pyramid?

12.

The grid of a pyramid is bases, of which the lateral faces are occupied by . What is the area of the base of the pyramid?

13.

Find the missing term x so that the sequence 2, 4, x, 16… is geometric. Calculate the sum of the first eight terms of the sequence.

14.

The volume of a square base pyramid is and the height is . What is the area of the base of the pyramid?

15.

The area of the base of a triangular base pyramid measures and the slant height . Calculate the total surface area of the pyramid.

16.

A pyramid has as its base as a rectangle with sides and . The slant height above the shorter side of the base measures , and above the longer base measures . Calculate the lateral surface area of the pyramid. Leave your result in square centimetres.

17.

The Egyptian pyramid captures of air and creates shadows beneath it. How far above the ground is the highest point of the pyramid?

18.

A quadrilateral base pyramid has as its base a rectangle with an aspect ratio of 5:3. The area of the base measures and the volume measures . Calculate the height of the pyramid.

19.

The lateral surface of an equilateral triangular base pyramid measures and the slant height is three times the length of the side of the base. Calculate the total surface area of the pyramid.

20.

The base area of a triangular base pyramid measures . What is the total surface area of a pyramid if the area of the base and the lateral surface area are in the ratio 1:3?

21.

The lateral surface area of a square base pyramid with length of one side of the base as measures . Calculate the height of the pyramid.

22.

In an equilateral triangular base pyramid, there is air. The height of the pyramid measures and its slant height . Calculate the lateral edge of the pyramid.

23.

The length of one side of the base of a square base pyramid measures and the height . Calculate the total surface area and volume of the pyramid.

24.

If a quadrilateral base pyramid is unfolded on a flat base, the area of the resulting figure measures . What is the lateral height of the pyramid if the area of the base is ?

25.

A small company has employees 8 men and 4 women. Four of them will attend the seminar.

In how many ways can they choose seminar participants to make gender representation equal?
How many ways can they choose seminar participants if more men than women have to attend the seminar?
What is the probability that all four participants in the randomly selected delegation will be of the same sex.