**Core Concept**
Medullary thyroid carcinoma (MTC) is a type of thyroid cancer that originates from the parafollicular cells (also known as C-cells) of the thyroid gland. These cells produce calcitonin, a hormone that helps regulate calcium levels in the blood. The presence of amyloid material in the aspirate is a characteristic feature of MTC, as amyloid deposits are produced by the abnormal C-cells.

**Why the Correct Answer is Right**
The management of MTC involves surgical removal of the tumor, typically a total thyroidectomy. This is because MTC is a malignant tumor that can spread to lymph nodes and distant sites. The presence of amyloid material in the aspirate confirms the diagnosis of MTC, and surgery is the primary treatment option. The correct answer is a total thyroidectomy, which is the standard surgical approach for MTC.

**Why Each Wrong Option is Incorrect**
**Option A:** Lobectomy is incorrect because it involves removal of only one lobe of the thyroid gland, which is not sufficient to treat MTC, which often involves both lobes of the gland.

**Option B:** Radioactive iodine therapy is incorrect because MTC does not take up radioactive iodine, making this treatment ineffective for MTC.

**Option C:** Chemotherapy is incorrect because MTC is typically resistant to chemotherapy, and surgery is the primary treatment option.

**Clinical Pearl / High-Yield Fact**
MTC can be hereditary, associated with multiple endocrine neoplasia type 2 (MEN2) syndrome. Patients with a family history of MTC or other MEN2-related cancers should be screened for MTC and other associated conditions.

**Correct Answer:** D. Total thyroidectomy