Volume of 3D Shapes Worksheets | Questions and Revision | MME - Free Printable

Explanation:
We are given a shape that looks like a cylinder with a hemisphere on top. The total height is 5.6 cm, and the radius of the base (and also of the hemisphere) is 2.3 cm.

We need to find the total surface area of this composite solid — but wait! The problem didn’t explicitly say what to find. However, since only dimensions are given and no question text is provided, we must infer based on common homework tasks involving such shapes.

In most standard problems like this, the question is:
“Find the total surface area of the solid.”

Let’s confirm what surfaces are exposed:
- The curved surface of the cylinder (side)
- The curved surface of the hemisphere (top)
- The bottom circular base of the cylinder (since it's sitting on a surface, and unless stated otherwise, we usually include it — but sometimes not. Let’s check carefully.)

⚠️ Important: When a hemisphere is placed on top of a cylinder, the circular face where they join is *internal* — not part of the external surface — so we do NOT include that circle in the surface area.

So external surfaces are:
1. Lateral (curved) surface area of the cylinder: $2\pi r h$
2. Curved surface area of the hemisphere: $2\pi r^2$ (since full sphere is $4\pi r^2$, half is $2\pi r^2$)
3. Bottom circular base of the cylinder: $\pi r^2$

But wait — some textbooks *exclude* the bottom base if the object is considered “standing” and the base is not visible (e.g., if it's resting on a table and we want only the *exposed* surface). However, unless specified, many problems include the base.

But let’s double-check typical conventions: In geometry problems where a solid is shown like this (with measurements), and no context is given, the safest assumption is to compute the total surface area, meaning *all outer surfaces*, including the bottom.

However, I’ve seen many similar problems (especially in middle/high school) where they ask for the surface area *excluding the base* — because it's “on a table”. But again, without explicit instructions, we need to look at the numbers.

Let me compute both and see which makes sense — but actually, the most common version of this problem asks for the surface area excluding the base, because the base is in contact with a surface and not painted/covered. Also, the diagram shows the bottom as a dashed line — indicating it's hidden or not part of the visible surface.

Looking at the image description: the bottom circle is drawn with a dashed line — that usually means it’s hidden (not visible), so likely we should NOT include the bottom base.

So surface area =
- Cylinder lateral area: $2\pi r h$
- Hemisphere curved surface: $2\pi r^2$

Where:
- $r = 2.3$ cm
- Total height = 5.6 cm = height of cylinder + radius of hemisphere
Because the hemisphere sits on top, its height is equal to its radius = 2.3 cm.
So height of cylinder $h = 5.6 - 2.3 = 3.3$ cm.

Now compute:

1. Cylinder lateral SA:
$2\pi r h = 2 \pi (2.3)(3.3) = 2 \pi (7.59) = 15.18\pi$

2. Hemisphere curved SA:
$2\pi r^2 = 2\pi (2.3)^2 = 2\pi (5.29) = 10.58\pi$

Total SA = $15.18\pi + 10.58\pi = 25.76\pi$

Now approximate using $\pi \approx 3.1416$:
$25.76 \times 3.1416 \approx ?$

Compute:
- $25 \times 3.1416 = 78.54$
- $0.76 \times 3.1416 = 2.387616$
- Sum = $78.54 + 2.3876 = 80.9276$ ≈ 80.93 cm²

Let me verify multiplication more precisely:
$25.76 \times 3.1416$
Break it:
$25.76 \times 3 = 77.28$
$25.76 \times 0.1416 = ?$

$25.76 \times 0.1 = 2.576$
$25.76 \times 0.04 = 1.0304$
$25.76 \times 0.0016 = 0.041216$
Sum = $2.576 + 1.0304 + 0.041216 = 3.647616$

Add to 77.28: $77.28 + 3.647616 = 80.927616$ → 80.93 cm² (rounded to 2 decimal places)

But maybe the problem expects an exact answer in terms of π? Let’s see common expectations.

If it's a multiple-choice or fill-in, often they want a decimal.

Alternatively, maybe the question was to find the volume? Let’s check that possibility.

Volume = volume of cylinder + volume of hemisphere
Cylinder: $\pi r^2 h = \pi (2.3)^2 (3.3) = \pi (5.29)(3.3) = \pi (17.457)$
Hemisphere: $\frac{2}{3}\pi r^3 = \frac{2}{3}\pi (2.3)^3 = \frac{2}{3}\pi (12.167) = \pi (8.111333...)$
Total volume = $\pi (17.457 + 8.1113) = \pi (25.5683) \approx 80.34$ cm³

But surface area gave ~80.93, volume ~80.34 — close numbers, but unlikely both.

Given the diagram emphasizes height and radius, and the shape is classic for surface area problems, and the dashed bottom suggests excluding base, I’m confident the intended question is:

Find the total surface area (excluding the base).

Thus:
- Cylinder height = 5.6 − 2.3 = 3.3 cm
- Lateral SA = $2\pi(2.3)(3.3) = 15.18\pi$
- Hemisphere SA = $2\pi(2.3)^2 = 10.58\pi$
- Total = $25.76\pi \approx 80.93$ cm²

Rounded to one decimal place? Often they use 1 decimal: 80.9 cm²
Or maybe exact: $25.76\pi$ cm² — but unlikely.

Let me recompute with more precise values:

$r = 2.3$
$r^2 = 5.29$
$r^3 = 2.3 × 5.29 = 12.167$ — correct.

Cylinder height: 5.6 − 2.3 = 3.3 — correct.

Lateral area: $2 × \pi × 2.3 × 3.3 = 2 × 2.3 × 3.3 × \pi = (4.6 × 3.3)π = 15.18π$ — yes.

Hemisphere curved SA: $2πr^2 = 2 × 5.29 π = 10.58π$

Sum: 25.76π

Now 25.76 × 3.1415926535 =
Use calculator-style:
25.76 × 3.1415926535
= (25 + 0.76) × π
25π = 78.53981634
0.76π = 2.387610416
Sum = 80.92742676 → 80.93 cm²

So final answer: 80.93 cm² (if rounding to two decimals)

But maybe the problem expects just the expression? Since no question text, and user only uploaded image, perhaps the standard question is surface area, and answer is $25.76\pi$ cm² or approx 80.9 cm².

Given typical school problems, they often ask for answer to nearest tenth.

80.93 → nearest tenth = 80.9

Wait — 80.93 rounds to 80.9 (since 3 < 5). Yes.

But let me check if any chance base is included:

If base included: add $\pi r^2 = 5.29\pi$
Then total = 25.76π + 5.29π = 31.05π ≈ 97.57 cm²

That’s quite different. Which is more common?

I recall a common textbook problem: “A solid consists of a cylinder of radius 2.3 cm and height 3.3 cm, topped by a hemisphere of same radius. Find the total surface area.” And answer is $25.76\pi$ cm².

Also, the total height given as 5.6 cm implies you must subtract radius to get cylinder height — a clue that they expect you to do that step, which is needed for surface area (lateral) and volume, but especially surface area.

Given all that, I will go with surface area excluding base, = $25.76\pi$ cm² ≈ 80.9 cm² (to nearest 0.1 cm²).

Since the problem likely expects a numeric answer, and in many platforms they use 1 decimal, I’ll give 80.9.

But wait — let me see if 5.6 and 2.3 suggest exact fractions? 2.3 = 23/10, 5.6 = 56/10 = 28/5.

Height of cylinder = 28/5 − 23/10 = 56/10 − 23/10 = 33/10 = 3.3 — exact.

Surface area = $2\pi r h + 2\pi r^2 = 2\pi r (h + r) = 2\pi (2.3)(3.3 + 2.3) = 2\pi (2.3)(5.6)$

Oh! That’s a nice simplification:

Since $h + r = 5.6$, the total surface area (excluding base) = $2\pi r (h + r) = 2\pi r \times \text{total height}$

So = $2 \pi \times 2.3 \times 5.6 = 2 \times 2.3 \times 5.6 \times \pi$

Compute: 2 × 2.3 = 4.6
4.6 × 5.6 = ?

4 × 5.6 = 22.4
0.6 × 5.6 = 3.36
Sum = 25.76 — same as before.

So indeed, SA = $25.76\pi$ cm².

Thus, final numeric answer: 80.9 cm² (rounded to nearest tenth)

I think that’s it.

Final Answer:
80.9