Question

The gold bar has a trapezium cross-sectional area. Gold has a density of 19.3 grams per cm3. Work out the mass of the gold bar. Give your answer in kilograms.

Answer 1

Answer:

Mass of gold bar = 13.896 kg

Step-by-step explanation:

Volume of gold bar = Area of  trapezium x Length of bar

Length of bar = 16 cm

Area of  trapezium = 2 x Area of triangle + Area of rectangle

Area of triangle = 0.5 x 5 x 3 = 7.5 cm²

2 x Area of triangle = 2 x 7.5 = 15 cm²

Area of rectangle = 6 x 5 = 30 cm²

Area of  trapezium = 15 + 30 = 45 cm²

Volume of gold bar = 45 x 16 = 720 cm³

Density of gold = 19.3 g/cm³

Mass of gold bar = 720 x 19.3 = 13896 g = 13.896 kg

Mass of gold bar = 13.896 kg

Answer 2

The mass of the gold bar is $\boxed{13.90{\text{ kg}}}.$

Further explanation:

The formula of area of trapezoid can be expressed as follows,

$\boxed{{\text{Area of trapezoid}} = \frac{1}{2} \times \left( {{\text{sum of parallel sides}}} \right) \times {\text{height}}}$

Given:

The height of the trapezium is $5{\text{ cm}}.$

The parallel sides of the trapezium are $6{\text{ cm and 12 cm}}.$

Explanation:

The area of the trapezium can be obtained as follows,

$\begin{aligned}{\text{Area}} &= \frac{1}{2} \times \left( {{\text{Sum of parallel sides}}} \right)\times h\\&= \frac{1}{2} \times \left( {6 + 12} \right) \times 5\\&= \frac{{18 \times 5}}{2}\\&= 9 \times 5\\&= 45{\text{ c}}{{\text{m}}^2}\\\end{aligned}$

The volume of gold bar can be obtained as follows,

$\begin{aligned}{\text{Volume}} &= \left( {{\text{Area of trapezium}}} \right) \times \left( {{\text{length of trapezium}}} \right)\\&= 45 \times 16\\&= 720{\text{ c}}{{\text{m}}^3}\\\end{aligned}$

The formula of the density can expressed as follows,

$\boxed{{\text{Density}} = \frac{{{\text{Mass}}}}{{{\text{Volume}}}}}$

The mass of the gold bar can be obtained as follows,

$\begin{aligned}19.3 &= \frac{{{\text{Mass}}}}{{{\text{720}}}}\\19.3 \times 720 &= {\text{Mass}}\\13900{\text{ g}} &= {\text{Mass}}\\13.90{\text{ kg}} &= {\text{Mass}}\\\end{aligned}$

The mass of the gold bar is $\boxed{13.90{\text{ kg}}}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: gold, gold bar, trapezium, cross-sectional, area, cross-sectional area, density, 19.3 grams, cm3, centimeter cube, mass, kilogram, mass of gold bar, diagonal, height, length of trapezium.