📐 geometry

1. The problem asks to find the circumference of a ball (sphere) given its volume of 5.6 dm³. 2. Recall the formula for the volume of a sphere: $$V = \frac{4}{3} \pi r^3$$ where $r

1. The problem is to find the volume of a shape or object given dimensions 5 and 6. 2. However, volume requires three dimensions (length, width, height) or a formula specifying the

1. The problem is to find the formula for the circumference of a circle. 2. The circumference is the distance around the circle.

1. **State the problem:** We need to find the slant height $l$ of a cone given its surface area $S = 204.2$ and radius $r = 5$. 2. **Recall the formula for the surface area of a co

1. **State the problem:** We are given two adjacent angles around a point, one is 70° and the other is $y$. We need to find the value of $y$. 2. **Use the fact that angles around a

1. **Stating the problem:** We have a right triangle ABC with right angle at C, where AC = 5.4 m, and a rectangle BCDE attached such that BC is perpendicular to AC and DE is parall

1. **Problem statement:** We have a regular pentagon ABCDE. - AP is the angle bisector of \(\angle BAE\).

1. **Problem statement:** Find the area of the cross section and the volume of each prism. ---

1. The first problem asks to find the distance using the formula $4^2 + 3^2$. 2. Calculate each square: $4^2 = 16$ and $3^2 = 9$.

1. The problem states that the scale of the office plan is 1:200, meaning 1 unit on the plan represents 200 units in real life. 2. The actual length of the wall is 5.8 meters. To f

1. **Calculate the value of g using tan 40° = 0.79** Given a right triangle with a 40° angle, the side adjacent to this angle is 10 cm, and the side opposite is g.

1. Problem: Given a circle with center O and various angles, find the angle $\alpha$ using the given data. **a)** Given angles 45° and 61°, find $\alpha$.

1. **State the problem:** We have a point B at coordinates $B(1,7)$. 2. The shape is enlarged about the center $C(3,7)$ by a scale factor of 3.

1. Problem 1: Given a circle with center O and various angles at the circumference or center, find angle $\alpha$ in each case. 1.a) Angle at circumference is 63°. $\alpha$ is the

1. **State the problem:** We have a shape with a point B at coordinates $(2, 7)$. The shape is enlarged by a scale factor of 3 about the center $(3, 7)$.

1. **State the problem:** We have three shapes X, Y, and Z. Shape X is translated by vector $$\begin{pmatrix} -2 \\ 5 \end{pmatrix}$$ to get shape Y. 2. Shape Y is then translated

1. **State the problem:** We need to determine if the point (2,9) can be the center of enlargement that maps the smaller cross centered at (4,7) to the larger cross centered at (9,

1. The problem states that triangle T is rotated 180° about the origin to form triangle T'. 2. The coordinates of vertex A of triangle T are given as (4, 7).

1. **State the problem:** We have a rectangle enlarged by a scale factor of $\frac{1}{3}$ with the center of enlargement at the red cross. We need to determine: a) Whether the new

1. The problem states that point \mathbf{R} was translated by the vector \begin{pmatrix} 4 \\ -3 \end{pmatrix} to get point \mathbf{R}'. 2. Translation means adding the vector to t

1. **State the problem:** We have triangle PQR with point S on segment QR. Given: $QP = QR = 9$ cm, $PR = PS = 6$ cm.