Question

Questions and their alternative answers are given. Choose the correct alternative answer.
(1) Find the circumference of a circle whose area is 1386 cm².
(A) 132 cm²
(B) 132 cm
(C) 42 cm
(D) 21 cm²
(2) The side of a cube is 4 m . If it is doubled, how many times will be the volume of the new cube, as compared with the original cube?
(A) Two times
(B) Three times
(C) Four times
(D) Eight times

Answer 1

(1) Area = 1386 cm2
$$\begin{gathered} \mathrm{\pi }{r}^2=1386 \\ \Rightarrow \frac{22}{7}{r}^2=1386 \\ \Rightarrow r^2=441 \\ \Rightarrow r=21\mathrm{cm} \end{gathered}$$
Circumference = $2\mathrm{\pi }r=2\times \frac{22}{7}\times 21=132\mathrm{cm}$
Hence, the correct answer is option B.

(2) Side of a cube = 4 m
Volume = $a^3=4^3=64{\mathrm{m}}^3$
New side = $2\times \mathrm{original}\mathrm{side}=2\times 4=8$ m
Volume of new cube = ${\left(8\right)}^3=512{\mathrm{m}}^3$
New volume = 512 m³ = $8\times 64=8\times \mathrm{old}\mathrm{volume}$
Thus, the new volume is 8 times the old volume.
Hence, the correct answer is option D.