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Solid Shapes: Types, Properties, and Formulas

Published: 12.08.2026·Updated: 14.08.2026

Nadia Rahmawati

Math Curriculum Team, Algonova

Solid Shapes: Types, Properties, and Formulas

A solid shape is a three-dimensional figure with length, width, and height, so it can be filled - meaning it has volume.

The difference from a plane shape: a plane shape answers how many tiles cover a floor, a solid answers how much water fits in a tank.

Seven Solids and Their Properties

Solid	Faces	Edges	Vertices	Volume
Cube	6	12	8	side × side × side
Cuboid	6	12	8	l × w × h
Triangular prism	5	9	6	base area × height
Square pyramid	5	8	5	⅓ × base area × height
Cylinder	3	2	0	π × r × r × h
Cone	2	1	1	⅓ × π × r × r × h
Sphere	1	0	0	⁴⁄₃ × π × r × r × r

Surface areas have their own pages: cube, cuboid, cylinder, cone, and sphere.

The Volume Pattern That Halves the Memorising

Seven volume formulas look like a lot. In fact there are only two patterns:

Prisms, cubes, cuboids, and cylinders are all base area times height. Only the base shape differs - square, rectangle, triangle, or circle.
Pyramids and cones are all one third of that. A cone is simply a pyramid with a circular base.

The sphere stands alone and does need memorising.

A child who catches this remembers two sentences rather than seven formulas. And the reason for the one third can be shown physically: three cones of water poured into a cylinder of the same base and height fill it exactly.

Surface Area Is Not Volume

Volume answers how much fits inside. Surface area answers how much paper you need to wrap it.

The units differ: volume in cubic units such as cubic centimetres, surface area in square units. If the final answer carries cubic units, it is volume.

Frequently Asked Questions

Does Algonova teach mathematics for primary, junior high, and senior high kids?

Yes, Algonova Indonesia offers a complete math program for kids aged 6 to 17, covering all school levels from primary, junior high, to senior high. Each level has a dedicated curriculum aligned with the child's cognitive stage and the Indonesian school curriculum (Kurikulum Merdeka). For primary school (6-12): basic operations, fractions, simple geometry, and introduction to algebra. For junior and senior high (13-17): algebra, quadratic equations, basic trigonometry, advanced geometry, basic calculus, statistics, UTBK SNBT preparation, and advanced topics. All classes are online live with certified teachers in small groups of up to 10 students per class. Our method is built on visual conceptual understanding, not formula memorisation. Try a free trial class for a child's level diagnostic and recommended learning path.

Is there a free trial class for kids math tutoring?

Yes. For mathematics Algonova Indonesia offers a free diagnostic session of about 60 minutes with no commitment. The format is called Metode Diagnostik Algonova. No credit card is needed and there is no auto subscription afterwards. Note that these roughly 60 minutes are a diagnostic session, not a regular class. A regular math class runs 90 minutes, while the coding and design tracks have their own introductory format, a free 60 minute master class. During the diagnostic a certified teacher maps the child's level: which topics are already solid and where the gaps sit. The child also tries the online learning platform and works through first problems matched to their school level. After the session parents receive a personal learning plan based on the diagnostic result, plus a transparent explanation of program, schedule, and pricing from Rp 102,000 per lesson. To book, fill in the form on the website.

How many students are in one Algonova math class?

Algonova Indonesia math classes come in three formats: 1-on-1 private, a mini-group of 2–4 kids, and a group of up to 10 students with similar ability and school grade levels. This small group format is deliberately chosen because it provides the optimal balance between social interaction with peers and personal teacher attention. In a mini-group, every child averages about 10 minutes of direct teacher interaction in a single session. Compare with traditional offline bimbel typically of 20-40 students per class — direct interaction there is only 1-2 minutes per child, or none at all. For families wanting full attention, one-on-one private class format is also available with one student per teacher. This format is more intensive and suits competition preparation, catching up from severe gaps, or specific topic depth.

How much does kids math tutoring at Algonova Indonesia cost?

Kids math tutoring at Algonova Indonesia starts from Rp 102,000 per lesson. The price includes a live session with a certified teacher, digital learning materials, online platform access, and an official certificate upon completing each program level. The transparent 'starting from' rate is the same across all school levels — the final quote depends only on class format (private, mini-group, or group) and how many sessions per week you choose. Groups are the most affordable option; private classes are more intensive and suit competition prep or closing larger gaps. Full pricing details are shared transparently after the free trial class. No surprise fees — every cost component is explained before formal enrolment. To receive the latest pricing details, fill in the booking form on the website.

Is math tutoring fully available online?

Yes, all Algonova Indonesia math programs are fully available online with live sessions taught by certified teachers — not recorded videos. Kids learn in real time in small groups of up to 10 students, with two-way interaction, live Q&A, and problems worked on alongside the teacher throughout the class. To join online class, a child only needs a computer or laptop with a camera, a stable internet connection, and a headset. The Algonova platform runs directly in the browser so no special software installation is required. Kids can write problems in a regular notebook or on a tablet with stylus. Because every class is fully online, families can join from anywhere in Indonesia and easily fit lessons around school and other activities.

What makes Algonova math tutoring effective for Indonesian kids?

Three main factors make Algonova math tutoring effective for Indonesian kids. First, the curriculum aligns with Kurikulum Merdeka used in national schools, so what is learned at Algonova directly helps with school lessons and exams. Second, the methodology is built on visual conceptual understanding (not formula memorisation). Kids learn to break big problems into small systematic steps — a thinking pattern transferable to other subjects like science and IT. Third, small groups of up to 10 students per class let teachers adjust pace to each child's ability. Slower kids get personal help, while faster kids don't get bored waiting. The result: most Algonova students see math grade improvements at school within the first 2-3 months.

What if my child is behind from earlier math grades?

Algonova Indonesia is specifically designed to help kids behind catch up in a way that doesn't make them feel defeated or ashamed. Every new student starts with a free diagnostic during the trial class to identify exactly where the gap occurred. Based on the diagnostic, the teacher builds a personal learning path that closes the gap from the most basic foundation. For example, a junior high student weak in algebra might actually be behind in primary school fraction operations. We go back to the foundation, then progress gradually without comparison with other peers. Many Algonova students who initially started 1-2 grade levels behind successfully caught up and even surpassed classmates within 3-6 months with weekly classes and consistent homework. It's never too late to start. Try a free trial class for diagnosis without commitment.

What is a solid shape?

A solid shape is a three-dimensional figure with length, width, and height, so it can be filled and therefore has volume. A plane shape answers how many tiles cover a floor; a solid answers how much water fits in a tank.

What are the types of solid shape?

Seven are taught at school: the cube, cuboid, prism, pyramid, cylinder, cone, and sphere.

How do you remember the seven volume formulas?

There are only two patterns. Prisms, cubes, cuboids, and cylinders are all base area times height - only the base shape differs. Pyramids and cones are all one third of that. Only the sphere stands alone and needs memorising.

Why are pyramid and cone volumes multiplied by one third?

It can be shown physically: three cones of water poured into a cylinder with the same base and height fill it exactly. That is why a cone's volume is one third of a cylinder's.

What is the difference between volume and surface area?

Volume answers how much fits inside; surface area answers how much paper is needed to wrap it. The units differ: volume in cubic units, surface area in square units. If the answer carries cubic units, it is volume.

Why do children struggle to picture solid shapes?

Usually not because they are weak at maths but because they are untrained at picturing space from a two-dimensional drawing. The remedy is not more exercises but real objects: a shoebox, a die, a tin, and a ball resolve more confusion in an hour than twenty practice questions.

Worked Volumes: Sphere, Cone and Prism

Sphere. V = 4/3 × π × r³. A sphere of radius 21 cm (π = 22/7): 21³ = 9,261, so V = 4/3 × 22/7 × 9,261 = 4/3 × 29,106 = 38,808 cm³. A hemisphere has volume 2/3 × π × r³. The volume of a sphere is exactly two thirds of the smallest cylinder that can hold it, one with radius r and height 2r.

Cone. V = ⅓ × π × r² × h. A party hat shaped like a cone with radius 7 cm and height 12 cm: V = ⅓ × 22/7 × 49 × 12 = ⅓ × 1,848 = 616 cm³. Forgetting the one third makes the answer three times too large.

Prism. V = base area × prism height. A triangular prism has two different heights: the height of the triangular base (used for the base area) and the height of the prism (the distance between the two ends). A triangular base with base 6 cm and height 4 cm, prism height 10 cm: base area = ½ × 6 × 4 = 12 cm², so V = 12 × 10 = 120 cm³. The surface area of a prism = 2 × base area + base perimeter × prism height.

Nets of Solids

A net is a solid opened out flat. A cube has eleven different nets, all of which fold back into a complete cube.

This chapter matters not because it is heavily tested but because it connects plane shapes to solids. Surface area is really just the total area of all the parts of the net - a child who has opened a box and measured each face stops experiencing the surface-area formula as memorisation.

Old cardboard, scissors, and glue settle this chapter faster than any diagram.

Where Children Get Stuck Most Often

Picturing a three-dimensional shape from a two-dimensional drawing. This is not a maths weakness but a spatial skill that needs separate practice.
Confusing volume with surface area. Check the units: cubic means volume.
Using the slant height as the height on a cone. The slant height runs from apex to base edge; the height is the perpendicular distance to the base centre. The two are linked by Pythagoras' theorem.
Forgetting the one third for pyramids and cones.

For problem one, the remedy is not more exercises but real objects. A shoebox, a die, a tin, and a ball resolve more confusion in an hour than twenty practice questions.

When It Is Taught at School

Year	What is covered
1–2	Recognising cubes, cuboids, spheres, cylinders
5	Volume of cubes and cuboids, nets
6	Prisms, pyramids, cylinders, cones, spheres
8	Flat-faced solids, surface area
9	Curved-surface solids
12	Three-dimensional geometry: distances and angles in space

Full topic lists are in Year 5, Year 6, and Year 9.

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