The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²): Option 1: 280 Option 2: 301.5 Option 3: 264 Option 4: 320.6

Answer: 264. Solution: To find the curved surface area of the cylinder, we first need to determine its height using the volume formula for a cylinder, which is given by: V = r^2 h Given that the volume V = 396 cm^3 and the radius r = 3 cm, we can substitute these values into the formula: 396 = (3^2) h This simplifies to: 396 = 9 h Now, solving for h: h = 396/(9) = 44/() cm Next, we use the formula for the curved surface area (CSA) of a cylinder, which is: CSA = 2 rh Substituting the values of r and h: CSA = 2 (3) (44/()) This simplifies to: CSA = 6 * 44 = 264 cm^2 Thus, the curved surface area of the cylinder is 264 cm^2.

Geometry

Solids

Medium

The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²):

280

301.5

264

320.6

✅ Correct Option: 3

To find the curved surface area of the cylinder, we first need to determine its height using the volume formula for a cylinder, which is given by:

$V = \pi r^2 h$

Given that the volume $V = 396 \, \text{cm}^3$ and the radius $r = 3 \, \text{cm}$ , we can substitute these values into the formula:

$396 = \pi (3^2) h$

This simplifies to:

$396 = 9\pi h$

Now, solving for $h$ :

$h = \frac{396}{9\pi} = \frac{44}{\pi} \, \text{cm}$

Next, we use the formula for the curved surface area (CSA) of a cylinder, which is:

$CSA = 2\pi rh$

Substituting the values of $r$ and $h$ :

$CSA = 2\pi (3) \left(\frac{44}{\pi}\right)$

This simplifies to:

$CSA = 6 \cdot 44 = 264 \, \text{cm}^2$

Thus, the curved surface area of the cylinder is $264 \, \text{cm}^2$ .

2023: 19 June Shift 1

A cone of height 24 cm and base radius 6 cm is made of modelling clay. A child reshapes it in the form of a sphere. The radius of the sphere is :

2025: 13 May Shift 2

Which of the following statements are true?

(A) If the diagonal of a cube is $6\sqrt{3}$ cm, then its volume and surface area are equal.

(B) If a rectangular block having dimensions 6 cm x 12 cm x 15 cm is cut into an exact number of equal cubes, then the least possible number of such cubes is 27.

Choose the correct answer from the options given below:

2026: 18 May Shift 2

Consider the surface area of the following solids.

A. A cube of edge 9 cm.

B. A cuboid of edges 18 cm, 14 cm and 7 cm.

C. A cylinder with radius of 14 cm and height 80 cm.

D. A sphere with radius of 14 cm.

Arrange the above in decreasing order.

2026: 20 May Shift 2

A cube has a total surface area of 384 $cm^2$ . What is the volume of the cube?

2023: 15 June Shift 2

Which of the following statements are incorrect?

(a) Volume of a cone = $\frac{1}{3}\pi r^3 h$

(b) Volume of a cone = $\frac{1}{3}\pi r^2 h$

(d) Volume of a hemisphere = $\frac{2}{3}\pi r^3$

(e) Volume of a cylinder = $\frac{1}{3}\pi r^3 h$

Choose the correct answer from the options given below:

2023: 24 May Shift 3

64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r.

The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²):

Solution

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