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 - Challenge Me

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

A soccer ball's surface area is 256π square cm. Bo wants its radius for a snug box. What is the radius, in cm?
A round balloon's surface area is 324π square inches. Esme wants its radius for a snug box. What is the radius, in inches?
Kira's glass pyramid has a square base 8 cm on a side. Its whole surface, base included, is 224 square cm. What is its slant height, in cm?
Luz's pyramid gift box has a square base 6 inches on a side. Its whole surface, base included, is 120 square inches. What is its slant height, in inches?
Milo's pyramid tent has a square base 10 feet on a side. Its whole surface, base included, is 280 square feet. What is its slant height, in feet?
Noah's castle roof model has a square base 12 inches on a side. Its whole surface, base included, is 504 square inches. What is its slant height, in inches?
The curved side of Pia's paper cone cup is 65π square cm. Its radius is 5 cm. How tall is it, straight up from the base to the tip, in cm?
The curved side of Ren's model volcano is 60π square inches. Its radius is 6 inches. How tall is it, straight up from the base to the tip, in inches?
The curved side of Tala's castle roof is 180π square cm. Its radius is 12 cm. How tall is it, straight up from the base to the tip, in cm?
The curved side of Zee's rocket's nose cone is 136π square cm. Its radius is 8 cm. How tall is it, straight up from the base to the tip, in 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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