Grade 10 · Math · Geometry

10th grade Volume of combined solids worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Volume of combined solids

Grade 10 Math Worksheet - Building Confidence

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Circle the best answer.

1.
Ari's silo is a cylinder 8 m across and 10 m tall, topped by a half-ball. Which expression gives its volume in m³?
- π·8²·10 + (2/3)π·8³
- π·4²·10 + (4/3)π·4³
- π·4²·10
- π·4²·10 + (2/3)π·4³
2.
Bo's toy rocket is a can 6 in across and 10 in tall with a cone tip 4 in tall. Which expression gives its volume in in³?
- π·3²·10 + (1/3)π·3²·4 = 102π
- π·3²·10 + π·3²·4 = 126π
- π·6²·10 + (1/3)π·6²·4 = 408π
- π·3²·10 = 90π
3.
A block is 10 cm by 8 cm by 6 cm. Esme drills a round hole 4 cm across straight through the 6 cm height. Which expression gives the volume left?
- 10·8·6 − π·2²·6 = 480 − 24π
- 10·8·6 = 480
- 10·8·6 − π·4²·6 = 480 − 96π
- 10·8·6 + π·2²·6 = 480 + 24π
4.
Jun's treat is a cone 6 cm across and 9 cm tall with a half-ball scoop of the same width on top. Which expression gives its volume?
- (1/3)π·3²·9 + (2/3)π·3³ = 45π
- π·3²·9 + (2/3)π·3³ = 99π
- (1/3)π·3²·9 + (4/3)π·3³ = 63π
- (1/3)π·6²·9 + (2/3)π·6³
5.
A funnel is a cone with radius 3 cm and slant height 5 cm. Luz finds the volume. What is it?
- 12π cm³: height √(5² − 3²) = 4 cm
- 36π cm³: π·3²·4, no third
- 15π cm³: height taken as the slant, 5 cm
- 4 cm: the height
6.
A pyramid has a square base 6 cm on a side. Each face has slant height 5 cm. Milo finds the volume. What is it?
- 144 cm³: 36 × 4, no third
- 48 cm³: height √(5² − 3²) = 4 cm
- 12 cm³: base area 3 × 3 = 9
- 60 cm³: height taken as the slant, 5 cm
7.
A cone-shaped pile has a base circumference of 18.84 m and slant height 5 m. Noah finds its volume with π = 3.14. What is it?
- 47.1 m³: height taken as the slant, 5 m
- 113.04 m³: no third
- 37.68 m³: r = 3 m, height 4 m
- 3 m: the radius
8.
Sketch, not to scale. A straight stack of coins has volume 100 cm³. Pia slides the coins so the stack leans, with the same coins and the same height. What is the volume now?
- Less than 100 cm³: the leaning stack looks smaller
- More than 100 cm³: the slanted side is longer
- 100 × cos of the lean angle, because the stack tilts
- Still 100 cm³: every layer keeps the same area
9.
Solid A is a box 4 by 3 by 10 cm. Solid B is 10 cm tall with curved sides, and every slice has area 12 cm². Ren compares them. What is true?
- B is larger: its curved surface is longer than the box's surface
- A is larger: a box looks bulkier
- A is 120 cm³, but B cannot be found without its shape
- Equal, 120 cm³ each, since every slice has the same area
10.
Sketch, not to scale. A sphere has radius 5 cm. A flat cut 3 cm from its center makes a circle. Zee finds the circle's area. What is it?
- 25π cm²: the sphere's biggest circle
- 34π cm²: radius √(5² + 3²)
- 9π cm²: radius 3
- 16π cm²: radius √(5² − 3²) = 4

10th grade Volume of combined solids worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Volume of combined solids. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can name the pieces of a combined solid, choose the right formula for each, and add or subtract their volumes.
I can find a height from a slant height, treat a frustum as a big cone minus a small one, and use Cavalieri's principle.
I can use scale factors for similar solids and work back from a total volume to a missing length.

Standard: G-GMD.A.3, G-MG.A.1

Words to know

composite solid: A solid made of simple pieces stuck together or with a hole.

frustum: A cone or pyramid with its tip cut off by a cut parallel to the base.

Cavalieri's principle: Solids of equal height with equal slice areas at every height have equal volume.

slant height: The length along a sloping face; the height runs straight up.

Common mistakes

Your child used the width for the radius, an area for a radius, or half of a side where the whole side belongs.

Your child left out the one third in a cone or pyramid.

Your child used the slant height as the height.

What to say

Ask: which length goes from the middle to the edge?

Ask: how many cones fill the matching can?

Ask: which length runs straight up, and which runs along the face?

Questions parents ask

What is the most common mistake with volume of combined solids?

Your child used the width for the radius, an area for a radius, or half of a side where the whole side belongs.

How can I help my child with volume of combined solids?

Ask: which length goes from the middle to the edge?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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