Grade 10 · Math · Geometry

10th grade Nets, and views of a solid from the top, front and side worksheet

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Nets, and views of a solid from the top, front and side

Grade 10 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Bo builds on a 3 by 3 base and records the front and right-side views on the card. What is the greatest number of cubes the building could have?
Esme builds on a 3 by 3 base and records the front and right-side views on the card. What is the greatest number of cubes the building could have?
3.
Jun slices a square pyramid parallel to its base. The base side is 12 cm, the height is 8 cm, and the cut is 2 cm above the base. What is the cross-section?
- A square with sides of 9 cm
- A triangle with a base of 9 cm
- A square with sides of 12 cm
- A square with sides of 3 cm
4.
Kira slices a cone parallel to its base. The base radius is 6 cm, the height is 9 cm, and the cut is 6 cm above the base. What is the cross-section?
- A circle with a radius of 4 cm
- A circle with a radius of 2 cm
- A circle with a radius of 6 cm
- An ellipse with axes of 4 cm and 6 cm
5.
Milo spins a 3 cm by 5 cm rectangle about its 5 cm side. What solid does it sweep out?
- A cylinder with radius 3 cm and height 5 cm, volume 15π cm³
- A cylinder with radius 5 cm and height 3 cm, volume 75π cm³
- A cone with radius 3 cm and height 5 cm, volume 15π cm³
- A cylinder with radius 3 cm and height 5 cm, volume 45π cm³
6.
Noah spins a right triangle with legs of 3 cm and 4 cm about its 4 cm leg. What solid does it sweep out?
- A cone with radius 3 cm and height 4 cm, volume 36π cm³
- A cone with radius 3 cm and height 4 cm, volume 12π cm³
- A cylinder with radius 3 cm and height 4 cm, volume 36π cm³
- A cone with radius 4 cm and height 3 cm, volume 16π cm³
7.
Pia spins a 2 cm by 6 cm rectangle about a line 1 cm from its long side. The line is parallel to the long side and outside the rectangle. What solid and volume result?
- A ring-shaped solid, outer radius 3 cm, inner radius 1 cm, height 6 cm, volume 24π cm³
- A ring-shaped solid, outer radius 7 cm, inner radius 1 cm, height 2 cm, volume 96π cm³
- A solid cylinder with radius 3 cm and height 6 cm, volume 54π cm³
- A ring-shaped solid, outer radius 3 cm, inner radius 1 cm, height 6 cm, volume 48π cm³
8.
Ren says the front and right-side views on the card fix a 3 by 3 building exactly. Which reply is justified?
- Yes: exactly 8 cubes, because the front view and the side view are added together
- No: between 4 and 10 cubes match both views, so the views do not fix the building
- Yes: exactly 4 cubes, because each unit of the front view is one cube in a fixed place
- Yes: as many as 12 cubes could be hidden behind the taller stacks
Read this first
Use this
Front view, tallest stack in each column from the left: 1, 3, 2. Right-side view, tallest stack in each row (row 1 on the left): 2, 1, 3.
9.
Tala says the front and right-side views on the card fix a 3 by 3 building exactly. Which reply is justified?
- No: between 6 and 14 cubes match both views, so the views do not fix the building
- Yes: exactly 6 cubes, because each unit of the front view is one cube in a fixed place
- Yes: exactly 12 cubes, because the front view and the side view are added together
- Yes: as many as 16 cubes could be hidden behind the taller stacks
10.
Zee says the front and right-side views on the card fix a 3 by 3 building exactly. Which reply is justified?
- Yes: as many as 18 cubes could be hidden behind the taller stacks
- No: between 8 and 16 cubes match both views, so the views do not fix the building
- Yes: exactly 13 cubes, because the front view and the side view are added together
- Yes: exactly 7 cubes, because each unit of the front view is one cube in a fixed place

10th grade Nets, and views of a solid from the top, front and side worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Nets, and views of a solid from the top, front and side. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the vertices of a solid from its faces, using that each edge is shared by two faces and V − E + F = 2.
I can tell whether a shape of six squares folds into a cube, and which solid two views describe.
I can name the cross-section of a solid cut by a plane, and find its size with similar figures or the Pythagorean theorem.
I can say what solid a flat shape sweeps out when it spins, and find its volume.
I can say when two views do not fix a building, and use Cavalieri's principle: equal slices at every height give equal volumes.

Standard: IXL parity (Nov 11) (nearest: G-GMD.B.4; 6.G.A.4)

Words to know

net: A solid unfolded flat into its faces

view: What a solid looks like from the top, front or side

face, edge, vertex: A flat surface; where two faces meet; a corner

cross-section: The flat shape you see where a plane cuts a solid

solid of revolution: The solid made by spinning a flat shape about a line

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

Common mistakes

Your child added up the sides of every face and used that as the number of edges. Each edge is shared by two faces, so halve the total first.

Your child stopped before adding 2 in V = E − F + 2.

Your child found the edges and stopped.

What to say

Ask: what does the formula say V − E + F equals?

Ask: which number does the question ask for, edges or vertices?

Questions parents ask

What is the most common mistake with nets, and views of a solid from the top, front and side?

Your child added up the sides of every face and used that as the number of edges. Each edge is shared by two faces, so halve the total first.

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.

More geometry

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