GRADE 10 SUBJECT - MATHEMATICS - WEEK 11 - LESSON 1 - Measurement - Solids

Sep 18, 2026

Grade 10 Mathematics Week 11 Lesson 1 focuses on measurement of solids. Students derive and apply surface area formulas for sphere, prism, cube, cylinder, pyramid, cone, and cuboid, including lateral/curved surface where relevant. The material defines key geometric terms such as radius, slant height, and height, then provides worked examples using substitutions and Pythagorean theorem for cone slant height. An exercise set practices solving problems with given dimensions and units, including cases using π approximations and finding missing radii, heights, or diameters.

LanguageEnglish

CategoryExam

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Measurement

Solids

Surface Area Formulae

Worked Examples

Exercise

GRADE 10 SUBJECT: MATHEMATICS WEEK 11 LESSON \# 1 TOPIC: Measurement SUB-TOPIC: Solids OBJECTIVES: Students will: 􀂙 derive formulae for areas 􀂙 calculate surface area CONTENT: Sphere Surface Area Formula A sphere is a solid figure where every point on the surface is equidistant from the center of the sphere. This distance is the radius, r, of the sphere. Surface area = 4πr2 Prism Surface Area Formula A prism is a geometric shape consisting of a stack of identical base shapes stacked on top of eachother to a depth d. This prism is a prism formed by a stack of triangles. Surface Area of a Prism = 2 × (Area of the base shape) + (Perimeter of base shape) × (d) Cube Surface Area Formula A cube is a special case box where all the sides are the same length. Surface Area of a Cube = 6a2 Cylinder Surface Area Formula A cylinder is a prism where the base shape is a circle. Surface Area of a Cylinder = 2πr2 + 2πrh Pyramid Surface Area Formula A pyramid is a solid shape consisting of a polygon base and triangular faces meeting at a common point above the base. Surface Area of a Pyramid = (sum of the areas of each face) + (area of the base) Surface Area of a Pyramid = (1»2 × Perimeter of base shape × s) + (Area of base shape) Surface area of a Square Pyramid = a2 + √3( a2 ) Surface Area Formula of a Cone A cone is a pyramid with a circular base with radius r and height h. The side length s can be found using the Pythagorean Theorem. s2 = r2 + h2 or s = √( r2 + h2 ) Surface Area of a Cone = πr2 + πrs Box (Cuboid) Surface Area Formula A box can be thought of a stack of rectangles L long and W wide piled on top of each other to a depth of D. Surface Area of a Box = Sum of the areas of each face of the box, or Surface Area of a Box = 2(L × W) + 2(L × D) + 2(W × D) Example1: Find the surface area of a cube with a side of length 3 cm Solution: Given that s = 3 Surface area of a cube = 6s2 = 6(3)2 = 54 cm2 How to find the surface area of a cube? Step 1: Find the length of aside Step 2: Substitute into the formula: side × side × 6 and evaluate Step 3: Write the units Example 2: The diameter of the base of a cylinder is 12 cm and the height is 8 cm. Find the surface area of the solid cylinder. Solution: Radius = 6 cm Surface area = 2πr (r + h) = = 528 cm2 Example 3: A cone has a radius of 3cm and height of 5cm, find total surface area of the cone. Solution: To begin with we need to find slant height of the cone, which is determined by using Pythagoras, since the cross section is a right triangle. l2 = h2 + r2 l2 = 52 + 32 l2 = 25 + 9 l = √(34) l = 5.83 cm And the total surface area of the cone is: SA = πr2 + πrl SA = π · r · (r + l) SA = π · 3 · (3 + 5.83) SA = 83.17 cm2 Example 4 : What is the total surface area of a sphere whose radius is 5.5 meters? Solution: Given that: r =5.5 Surface area of the sphere: SA = 4 × π × r2 SA = 4 × π × (5 .5)2 SA = 4 × 3.14 × 30.25 SA = 379.94 Thus the surface area of the sphere is 379.94 m2. Example 5: Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm. TSA = 2 (lw + wh + hl) TSA = 2 (8*6 + 6*5 + 5*8) TSA = 2 (48 + 30 + 40) TSA = 236 So, the total surface area of this cuboid is 236 cm2. EXERCISE: 1. Height and radius of the cone is 5 yard and 7 yard. Find the lateral surface area of the given cone. 2. The slant height of a cone is 20cm. the diameter of the base is 15cm. Find the curved surface area of cone. 3. What is the total surface area of a cone if its radius = 4cm and height = 3 cm. 4. The total surface area of a cone is 375 square inches. If its slant height is four times the radius, then what is the base diameter of the cone? Use π = 3. 5. Height and radius of the cone is 5 yard and 7 yard. Find the lateral surface area of the given cone. 6. A circular cone is 15 inches high and the radius of the base is 20 inches. What i

FAQs

What is the sphere surface area formula used in this lesson?

The sphere surface area is given by SA = 4πr2, where r is the radius.

How do you find the slant height of a cone in these examples?

Use the Pythagorean theorem with l2 = h2 + r2, then take l = √(h2 + r2).

What formulas are used to calculate the surface area of a cylinder?

The lesson uses SA = 2πr2 + 2πrh for total surface area, and it also applies lateral/curved surface questions in the exercise.

Sep 18, 2026

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