Identify the given inside radius and wall thickness.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the questions:

1.1.1

Identify the given inside radius and wall thickness.
The inside radius is $r_{inside} = 21 \text{ cm}$ .
The wall thickness is $1 \text{ cm}$ .
Calculate the outside radius.
The outside radius is the inside radius plus the wall thickness.
$r_{outside} = r_{inside} + \text{wall thickness}$ $r_{outside} = 21 \text{ cm} + 1 \text{ cm}$ $r_{outside} = 22 \text{ cm}$
The radius of the outside circle is $\boxed{\text{22 cm}}$ .

1.1.2
Identify the inside radius.
The inside radius is $r_{inside} = 21 \text{ cm}$ .
Calculate the diameter of the inside circle.
The diameter is twice the radius.
$D_{inside} = 2 \times r_{inside}$ $D_{inside} = 2 \times 21 \text{ cm}$ $D_{inside} = 42 \text{ cm}$
The diameter of the inside circle is $\boxed{\text{42 cm}}$ .

1.1.3
Identify the given values for radius, height, and $\pi$ .
The inside radius is $r = 21 \text{ cm}$ .
The height is $h = 35 \text{ cm}$ .
Use $\pi = 3.14$ .
Calculate the volume of the inside of the container using the formula $V = \pi r^2 h$ .
$V = \pi r^2 h$ $V = 3.14 \times (21 \text{ cm})^2 \times 35 \text{ cm}$ $V = 3.14 \times 441 \text{ cm}^2 \times 35 \text{ cm}$ $V = 3.14 \times 15435 \text{ cm}^3$ $V = 48465.9 \text{ cm}^3$
The volume of the inside of the container is $\boxed{\text{48465.9 cm}^3}$ .

1.1.4
Calculate 55% of the total capacity (volume from 1.1.3).
Total capacity $V = 48465.9 \text{ cm}^3$ .
Amount of oil = $55\%$ of $V$ .
$\text{Amount of oil in cm}^3 = 0.55 \times 48465.9 \text{ cm}^3$ $\text{Amount of oil in cm}^3 = 26656.245 \text{ cm}^3$
Convert the amount of oil from $\text{cm}^3$ to litres.
Given $1 \text{ litre} = 1000 \text{ cm}^3$ .
$\text{Amount of oil in litres} = \frac{26656.245 \text{ cm}^3}{1000 \text{ cm}^3/\text{litre}}$ $\text{Amount of oil in litres} = 26.656245 \text{ litres}$
Rounding to two decimal places, the amount of oil in litres is $\boxed{\text{26.66 litres}}$ .

1.1.5
Identify the amount of oil in litres and the cost per litre.
Amount of oil = $26.656245 \text{ litres}$ (from 1.1.4).
Cost per litre = R $13.00$ .
Calculate the total cost.
$\text{Total cost} = \text{Amount of oil in litres} \times \text{Cost per litre}$ $\text{Total cost} = 26.656245 \text{ litres} \times \text{R}13.00/\text{litre}$ $\text{Total cost} = \text{R}346.531185$
Rounding to two decimal places, the total cost is $\boxed{\text{R346.53}}$ .

Identify the given inside radius and wall thickness.

Step-by-step solution

1.1.1

Identify the given inside radius and wall thickness.

Calculate the outside radius.

1.1.2

Identify the inside radius.

Calculate the diameter of the inside circle.

1.1.3

Identify the given values for radius, height, and $\pi$ .

Calculate the volume of the inside of the container using the formula $V = \pi r^2 h$ .

1.1.4

Calculate 55% of the total capacity (volume from 1.1.3).

Convert the amount of oil from $\text{cm}^3$ to litres.

1.1.5

Identify the amount of oil in litres and the cost per litre.

Calculate the total cost.

Still stuck on this one?

More Mathematics Questions

Identify the given inside radius and wall thickness.

Step-by-step solution

1.1.1

Identify the given inside radius and wall thickness.

Calculate the outside radius.

1.1.2

Identify the inside radius.

Calculate the diameter of the inside circle.

1.1.3

Identify the given values for radius, height, and π\piπ.

Calculate the volume of the inside of the container using the formula V=πr2hV = \pi r^2 hV=πr2h.

1.1.4

Calculate 55% of the total capacity (volume from 1.1.3).

Convert the amount of oil from cm3\text{cm}^3cm3 to litres.

1.1.5

Identify the amount of oil in litres and the cost per litre.

Calculate the total cost.

Still stuck on this one?

More Mathematics Questions

Identify the given values for radius, height, and $\pi$ .

Calculate the volume of the inside of the container using the formula $V = \pi r^2 h$ .

Convert the amount of oil from $\text{cm}^3$ to litres.