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

NameDate

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

Bo's model pyramid is a square pyramid: base 14 cm on a side, height 24 cm straight up. What is its total surface area, base included, in square cm?
Esme's castle roof is a square pyramid: base 16 inches on a side, height 15 inches straight up. What is its total surface area, base included, in square inches?
Jun's sand pyramid model is a square pyramid: base 18 cm on a side, height 12 cm straight up. What is its total surface area, base included, in square cm?
Kira paints a solid clay ice cream cone, base and all. Radius 5 cm, height 12 cm. What is its total surface area in square cm, in terms of π (like 14π)?
Luz paints a solid model volcano, base and all. Radius 6 inches, height 8 inches. What is its total surface area in square inches, in terms of π (like 14π)?
Noah paints a solid rocket's nose cone, base and all. Radius 9 cm, height 12 cm. What is its total surface area in square cm, in terms of π (like 14π)?
Pia wraps half an orange, a half-ball with radius 2 cm, flat side too. Using π = 3.14, what is its total surface area in square cm?
Ren wraps half of a small watermelon, a half-ball with radius 5 inches, flat side too. Using π = 3.14, what is its total surface area in square inches?
Tala wraps a solid half-ball of clay with radius 6 cm, flat side too. Using π = 3.14, what is its total surface area in square cm?
Zee wraps a solid model igloo, a half-ball with radius 3 cm, flat side too. Using π = 3.14, what is its total surface area in square cm?

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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