# Recent questions tagged geometry

A wire would enclose an area of $1936 \: m^2$, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters? $1096$ $1111$ $1243$ $2486$
A rectangle becomes a square when its length and breadth are reduced by $10$ m and $5$ m, respectively. During this process, the rectangle loses $650 m^2$ of area. What is the area of the original rectangle in square meters? $1125$ $2250$ $2924$ $4500$
A right-angled cone (with base radius $5$ cm and height $12$ cm), as shown in the figure below, is rolled on the ground keeping the point $P$ fixed until the point $Q$ (at the base of the cone, as shown) touches the ground again. By what angle (in radians) about $P$ does the cone travel? $\dfrac{5\pi}{12} \\$ $\dfrac{5\pi}{24} \\$ $\dfrac{24\pi}{5} \\$ $\dfrac{10\pi}{13}$