Grade 10 · Math · Geometry

10th grade Lateral and total surface area of pyramids, cones and spheres worksheet

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Lateral and total surface area of pyramids, cones and spheres

Grade 10 Math Worksheet - Building Confidence

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a square base 6 cm by 6 cm with four triangles folded out, each with slant height 5 cm. Ari covers the sides of a paper pyramid: base 6 cm on a side, slant height 5 cm. What is its lateral area (side faces only), in square cm?
a square base 10 inches by 10 inches with four triangles folded out, each with slant height 12 inches. Esme covers the sides of a castle roof: base 10 inches on a side, slant height 12 inches. It is a square pyramid. What is its lateral area (side faces only), in square inches?
a square base 4 inches by 4 inches with four triangles folded out, each with slant height 9 inches. Jun covers the sides of a pyramid gift box: base 4 inches on a side, slant height 9 inches. What is its lateral area (side faces only), in square inches?
Kira's paper ice cream cone has radius 3 cm and slant height 7 cm. What is its lateral area (the curved side only) in square cm, in terms of π (like 14π)?
Milo's castle tower's cone roof has radius 5 cm and slant height 8 cm. What is its lateral area (the curved side only) in square cm, in terms of π (like 14π)?
Noah's rocket's nose cone has radius 6 cm and slant height 11 cm. What is its lateral area (the curved side only) in square cm, in terms of π (like 14π)?
Pia's toy ball is 4 cm across. What is its surface area in square cm, in terms of π (like 14π)?
Ren's orange is 10 cm across. What is its surface area in square cm, in terms of π (like 14π)?
Tala's round balloon is 14 inches across. What is its surface area in square inches, in terms of π (like 14π)?
Zee's basketball is 18 cm across. What is its surface area in square cm, in terms of π (like 14π)?

10th grade Lateral and total surface area of pyramids, cones and spheres worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Surface area of pyramids, cones and spheres. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the side faces only (lateral area) and the whole surface of a pyramid or cone.
I can find the slant height from the height with the Pythagorean theorem.
I can find a sphere's or half-ball's surface, and work back from an area to a length.

Standard: G-MG.A.1

Words to know

lateral area: The side faces only, without the base.

total surface area: Every face of the net, base included.

slant height (ℓ): The height of a side face, measured along the face.

height (h): Straight up inside the solid, from the base's middle to the tip.

hemisphere: Half a ball; a solid one also has a flat circle face.

Common mistakes

Your child used a whole rectangle for each triangle face instead of half of it. Draw one triangle face inside a rectangle and ask how much of the rectangle it covers.

Your child added the base when only the side faces were asked for.

Your child found the area of one triangle face and stopped.

What to say

Ask: which faces would you paint if the base sits on the table?

Ask: how many side faces does a square pyramid have?

Questions parents ask

What is the most common mistake with lateral and total surface area of pyramids, cones and spheres?

Your child used a whole rectangle for each triangle face instead of half of it. Draw one triangle face inside a rectangle and ask how much of the rectangle it covers.

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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