Interactive multiple-choice quiz: Volume of Spheres and Hemispheres
This educational resource focuses on calculating the volume of spheres and hemispheres. It includes various problems involving radius and diameter, real-world applications like spherical beads and pearls, and calculating inflation time based on volume and rate. Ideal for students practicing geometry and spatial measurement concepts.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Find the volume of the hemisphere. Round to the nearest tenth.
Explanation
The volume of a hemisphere is given by $V = \frac{2}{3} \pi r^3$. With r = 6.7, $V = \frac{2}{3} \pi (6.7)^3 \approx 629.6 \text{ ft}^3$.
Question 2
DB ID: 5445
Points: 1
Find the volume of the hemisphere. Round to the nearest tenth.
Explanation
The radius shown is 12 mm. For a hemisphere, $V = \frac{2}{3} \pi r^3 = \frac{2}{3} \pi (12)^3 \approx 3617.3 \text{ mm}^3$.
Question 3
DB ID: 5446
Points: 1
Olga is using spherical beads to create a border on a picture frame. Each bead has a diameter of 1.5 millimeters. Find the volume of each bead. Round to the nearest tenth.
Explanation
The diameter is 1.5, so the radius r = 0.75. The volume of a sphere is $V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.75)^3 \approx 1.8 \text{ mm}^3$.
Question 4
DB ID: 5447
Points: 1
What is the volume of the sphere shown? (Use 3.14 for $\pi$.)
Explanation
Using $V = \frac{4}{3} \pi r^3$ with r = 48 and $\pi = 3.14$, the volume is $V = \frac{4}{3} \cdot 3.14 \cdot 48^3 \approx 463011.8 \text{ mm}^3$.
Question 5
DB ID: 5448
Points: 1
Find the volume of the sphere. Express your answer in terms of $\pi$.
Explanation
With a radius of r = 23, the volume is $V = \frac{4}{3} \pi (23)^3 = \frac{4}{3} \pi (12167) \approx 16222.7\pi \text{ ft}^3$.
Question 6
DB ID: 5449
Points: 1
Find the volume of the sphere. Express your answer in terms of $\pi$.
Explanation
The diameter is 9 inches, so the radius is r = 4.5. The volume $V = \frac{4}{3} \pi (4.5)^3 = 121.5\pi \text{ in}^3$.
Question 7
DB ID: 5450
Points: 1
A necklace has a single spherical pearl with a radius of 2.1 millimeters. What is the volume of the pearl? Round to the nearest tenth.
Explanation
The volume is calculated using $V = \frac{4}{3} \pi (2.1)^3 \approx 38.8 \text{ mm}^3$.
Question 8
DB ID: 5451
Points: 1
The radius of a mini-basketball is 4 inches. A pump can inflate the ball at a rate of 6 cubic inches per second. How long will it take to inflate the ball? Round to the nearest tenth.
Explanation
First find the volume: $V = \frac{4}{3} \pi (4)^3 \approx 268.08 \text{ in}^3$. Divide by the rate: $268.08 / 6 \approx 44.7$ seconds.
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يمكنك تسجيل الدخول لحفظ سجل محاولاتك، معرفة أخطائك المتكررة، والحصول على نصائح مخصصة. تسجيل الدخول باستخدام Google
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