Question

question 12
a right cylinder has a radius of 5 and a height of 9. what is its surface area?
a. $70\pi$ units$^2$
b. $140\pi$ units$^2$
c. $45\pi$ units$^2$
d. $90\pi$ units$^2$

question 13
a right cone has a slant height of 6 and a radius of 4. what is its surface area?
a. $24\pi$ units$^2$
b. $56\pi$ units$^2$
c. $16\pi$ units$^2$
d. $40\pi$ units$^2$

question 14
what is the volume of the prism given below?
a. 350 units$^3$
b. 600 units$^3$
c. 1200 units$^3$
d. 520 units$^3$

question 15
what is the volume of the cylinder shown below?
a. $1452\pi$ units$^3$
b. $1112\pi$ units$^3$
c. $132\pi$ units$^3$
d. $121\pi$ units$^3$

Explanation:

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Question 12

Step1: Recall cylinder surface area formula

The total surface area of a right cylinder is $SA = 2\pi r^2 + 2\pi r h$, where $r$ is radius, $h$ is height.

Step2: Substitute $r=5$, $h=9$

$SA = 2\pi (5)^2 + 2\pi (5)(9)$

Step3: Calculate each term

$2\pi(25) = 50\pi$, $2\pi(45)=90\pi$

Step4: Sum the terms

$SA = 50\pi + 90\pi = 140\pi$

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Question 13

Step1: Recall cone surface area formula

The total surface area of a right cone is $SA = \pi r^2 + \pi r l$, where $r$ is radius, $l$ is slant height.

Step2: Substitute $r=4$, $l=6$

$SA = \pi (4)^2 + \pi (4)(6)$

Step3: Calculate each term

$\pi(16)=16\pi$, $\pi(24)=24\pi$

Step4: Sum the terms

$SA = 16\pi + 24\pi = 40\pi$

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Question 14

Step1: Recall prism volume formula

Volume of a prism is $V = B \times h$, where $B$ is area of the base, $h$ is length of the prism.

Step2: Calculate triangular base area

The base is a triangle: $B = \frac{1}{2} \times 15 \times 8 = 60$

Step3: Substitute $B=60$, $h=10$

$V = 60 \times 10 = 600$

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Question 15

Step1: Recall cylinder volume formula

Volume of a cylinder is $V = \pi r^2 h$, where $r$ is radius, $h$ is height.

Step2: Substitute $r=11$, $h=12$

$V = \pi (11)^2 (12)$

Step3: Calculate the value

$V = \pi (121)(12) = 1452\pi$

Answer:

Question 12: B. $140\pi$ units$^2$
Question 13: D. $40\pi$ units$^2$
Question 14: B. $600$ units$^3$
Question 15: A. $1452\pi$ units$^3$