Question: The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^2. If a spherical balloon has a volume of 972 pi cubic centimetres, what is the surface area of the balloon in square centimetres?
- 40
- 100
- 400
- 1,000
- 10,000
“The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^2.”- is the topic from the GMAT Quantitative problem set. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
This question has only one approach.
Given to us that the volume of a sphere with radius r is (\(\frac{4}{3}\))*pi*r^3 and the surface area is 4*pi*r^2. It is given that the volume of the balloon is 972 pi cubic centimetres. It is asked to find out the surface area of the balloon.
he surface area of the balloon which is assumed to be a sphere will be
4*pi*r^2.
But we do not know the radius of the sphere.
Therefore the first step is to find out the radius.
Given volume = 972pi cm^3
From the given formula we get,
(\(\frac{4}{3}\))*pi*r^3 = 972 pi cm^3
\(\frac{4}{3}\) \(r^3\) = 972 \(cm^3\)
\(r^3\) = \(\frac{3}{4}\) * 972 \(cm^3\)
\(r^3\) = 3 * 243 \(cm^3\)
\(r^3\) = 729 \(cm^3\)
we get , r = \(\sqrt[3]{729cm^3}\) = 9 cm
Now putting this value of r in the formula of surface area,
Surface area = 4\(\pi r^2\) = 4 *\(\pi\)* \((9cm)^2\) = 36 * 4 * \(\pi\)\(cm^2\) = 243 \(cm^2\)
243 is approximately 1000.
Correct Answer: D
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