Mensuration Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

According to question

$A_1/A_2 = {π r_1^2}/{πr_2^2} = 1/2$

⇒ $(r_1/r_2)^2 = 1/2$ ...(i)

As, Circles are bent in the form of square then their perimeter will become equal.

$2πr_1 = 4a_1$

⇒ $a_1 = {πr_1}/2$

Similarly, $a_2 = {π r_2}/2$

∴ $A_1/A_2 = a_1^2/a_2^2 = {({π r_1}/2)^2}/{({π r_2}/2)^2} = r_1^2/r_2^2 = 1/2$[from Eq. (i)]

Answer: (a)

As per the given condition, the radius of sphere and cylinder will be same.

Volume of cylinder = $πR^2H = πR^2 .D = 2πR^3$

(where R = Radius)

Volume of sphere $V_s = 4/3 π R^3$

⇒ = ${V_S}/V ={4/3 π R^3}/{2π R^3} = 2/3 ⇒ V_s = 2/3 V$

Answer: (a)

∠BAC = ∠BDC {Angle made by same chord BC in the same side}

Now, from ΔBCD, sum of angles = 180°

∠CBD + ∠BDC + ∠BCD = 180°

∴ ∠BCD = 180° – 100° = 80°