Question

A telescope shows an asteroid of width 8181 km as an image of width 27 mm. Calculate the width of an asteroid whose image measures 5 mm wide.

• A. 303 km
• B. 606 km
• C. 1212 km
• D. 1515 km

Answer 1

The correct option is D 1515 km

A telescope shows an asteroid of width 8181 km as an image of width 27 mm.

∴ The "width" of an asteroid whose image is 1 mm wide will be calculated by:
$8181km÷27mm$.

The number $8181$ in its expanded form will be:
$8181=8000+100+80+1$.

So, calculating $8181km÷27mm$ using the box method,

Adding the partial quotients together, the final quotient will be: $200+100+2+1=303$.

∴ The real width of an asteroid whose image is 1 mm wide will be $303$ km.

So, the width of an asteroid whose image is $5mm$ will be given by $303\times 5=1515km$.