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SSC CHSL 2022 PYQ — Question 67

SSC CHSL - 26 May 2022 - Shift 3 • Quantitative Aptitude • Q67

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15 identical solid spherical balls of radius 5 cm are melted to form a single sphere. In this process, 35% of the mass is wasted. What is the radius (in cm) of the single sphere that is now formed? [Use π = 22/7, and give your answer correct to two decimal places.]

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 10.68 cm

 

Let the radius of the single sphere be R.

Since 35 % of the sphere is wasted, 65 % would have been used for transforming.

65% of 15 × (Volume of identical solid spherical balls having radius 5cm) = volume of a single sphere 

0.65×15×43×π×53=43×π×R3⇒0.65×15×53=R3⇒1218.75=R3⇒R=(1218.75)1/3\begin{aligned} & 0.65 \times 15 \times \frac{4}{3} \times \pi \times 5^3=\frac{4}{3} \times \pi \times R^3 \\ & \Rightarrow 0.65 \times 15 \times 5^3=R^3 \\ & \Rightarrow 1218.75=R^3 \\ & \Rightarrow R=(1218.75)^{1 / 3} \end{aligned}

⇒ R = 10.68 cm

∴ The radius of the single sphere is 10.68 cm.