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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Three-dimensional (3D) shapes

Grade: 6-a Lesson: S4-L2

Explanation: Let us verify the answer here with the steps.

Lesson Steps Head1

Step	Type	Explanation	Answer
1	Problem	A conical tank with a radius of 9 meters and a height of 12 meters is to be painted on the inside. Calculate the total surface area of the inside of the tank that needs to be painted.
2	Step	The given values are	r = 9 m , h = 12 m
3	Formula	Lateral Surface Area (A) = \$"π" times "r" times "l"\$	\$"A" = π times "r" times "l"\$
4	Formula	Pythagorean theorem, as the height (h), radius (r), and slant height (l) form a right triangle	\$l^2 = r^2 + h^2\$
5	Step	Now, plug these values into the formula	\$l^2 = 9^2 + 12^2\$ \$l^2 = 225\$ l = 15
6	Formula	To calculate the total surface area A	\$A = πr(r+l)\$
7	Step	Now plug the values in the formula	\$A = π times 9(9 + 15)\$
8	Step	After simplification	A = 216π sq.m
9	Step	So, the total surface area of the inside of the tank that needs to be painted is 216π sq.m.
10	SumUp	Can you summarize what you’ve understood in the above steps?
11	Choice.A	This is incorrect. It’s likely a result of adding the base area and lateral area incorrectly	201π sq.m
12	Choice.B	This is incorrect. It’s likely a miscalculation of the lateral surface area	261π sq.m
13	Choice.C	This is incorrect. It’s also likely a miscalculation of the lateral surface area	210π sq.m
14	Choice.D	This option is correct because it correctly calculates the total surface area of the inside of the tank	216π sq.m
15	Answer	Option	D
16	SumUp	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

A conical tank with a radius of 9 meters and a height of 12 meters is to be painted on the inside. Calculate the total surface area of the inside of the tank that needs to be painted.

Step

The given values are

r = 9 m , h = 12 m

Formula

Lateral Surface Area (A) = \$"π" times "r" times "l"\$

\$"A" = π times "r" times "l"\$

Formula

Pythagorean theorem, as the height (h), radius (r), and slant height (l) form a right triangle

\$l^2 = r^2 + h^2\$

Step

Now, plug these values into the formula

\$l^2 = 9^2 + 12^2\$

\$l^2 = 225\$

l = 15

Formula

To calculate the total surface area A

\$A = πr(r+l)\$

Step

Now plug the values in the formula

\$A = π times 9(9 + 15)\$

Step

After simplification

A = 216π sq.m

Step

So, the total surface area of the inside of the tank that needs to be painted is 216π sq.m.

SumUp

Can you summarize what you’ve understood in the above steps?

Choice.A

This is incorrect. It’s likely a result of adding the base area and lateral area incorrectly

201π sq.m

Choice.B

This is incorrect. It’s likely a miscalculation of the lateral surface area

261π sq.m

Choice.C

This is incorrect. It’s also likely a miscalculation of the lateral surface area

210π sq.m

Choice.D

This option is correct because it correctly calculates the total surface area of the inside of the tank

216π sq.m

Answer

Option

SumUp

Can you summarize what you’ve understood in the above steps?